# ===== Imports =====

# ===== General =====
import numpy as np
import pandas as pd
import math
import warnings
warnings.filterwarnings('ignore')

# ===== Visualization =====
import seaborn as sns
import missingno as msno
import matplotlib.pyplot as plt
import scipy.stats as stats
from matplotlib import patheffects
from matplotlib.colors import LinearSegmentedColormap
import matplotlib.patches as mpatches
import matplotlib.colors as mcolors
import matplotlib.patheffects as path_effects
%matplotlib inline

# ===== Hypotheses testing =====
from scipy.stats import chi2_contingency
from scipy import stats
from scipy.stats import f_oneway
from scipy.stats import pearsonr

# ===== Preprocessing =====
from sklearn.preprocessing import StandardScaler, LabelEncoder, OneHotEncoder, OrdinalEncoder
from sklearn.impute import SimpleImputer
from sklearn.compose import ColumnTransformer
from category_encoders import CountEncoder
from sklearn.pipeline import Pipeline

# ===== Outlier Influence =====
from statsmodels.stats.outliers_influence import variance_inflation_factor
from statsmodels.tools.tools import add_constant
import statsmodels.api as sm

# ===== Imbalanced handling =====
from imblearn.over_sampling import SMOTE

# ===== Model Selection =====
import time
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
from sklearn.linear_model import Ridge
from sklearn.linear_model import Lasso
from sklearn.ensemble import RandomForestRegressor
from xgboost import XGBRegressor
from lightgbm import LGBMRegressor

# ===== Evaluation Metrics =====
from sklearn.metrics import mean_absolute_error, mean_squared_error, r2_score
from sklearn.model_selection import cross_val_score, KFold
from sklearn.metrics import (mean_squared_error, mean_absolute_error, r2_score, explained_variance_score, mean_absolute_percentage_error)
from sklearn.model_selection import cross_val_score, KFold
from sklearn.model_selection import RandomizedSearchCV

# ===== Load Data =====
df = pd.read_excel('Flight_Fare.xlsx')

# ===== Checking first five rows of dataset =====
df.head(5)

# ===== Checking last five rows of dataset =====
df.tail(5)

# ===== Basic Overview =====

# ===== To view the summary stats of numerical columns =====
df.describe()

# ===== To View the categorical columns =====
df.describe(include='O').T

# ===== Checking the info of dataset =====
df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 10683 entries, 0 to 10682
Data columns (total 11 columns):
 #   Column           Non-Null Count  Dtype 
---  ------           --------------  ----- 
 0   Airline          10683 non-null  object
 1   Date_of_Journey  10683 non-null  object
 2   Source           10683 non-null  object
 3   Destination      10683 non-null  object
 4   Route            10682 non-null  object
 5   Dep_Time         10683 non-null  object
 6   Arrival_Time     10683 non-null  object
 7   Duration         10683 non-null  object
 8   Total_Stops      10682 non-null  object
 9   Additional_Info  10683 non-null  object
 10  Price            10683 non-null  int64 
dtypes: int64(1), object(10)
memory usage: 918.2+ KB

# ===== Checking the no. of rows and columns =====
df.shape

(10683, 11)

# ===== Domain Analysis =====
df.columns

Index(['Airline', 'Date_of_Journey', 'Source', 'Destination', 'Route',
       'Dep_Time', 'Arrival_Time', 'Duration', 'Total_Stops',
       'Additional_Info', 'Price'],
      dtype='object')

# ===== Change the dtypes and column names =====
# ===== Convert Date_of_Journey =====
df['Date_of_Journey'] = pd.to_datetime(df['Date_of_Journey'], format='%d/%m/%Y', errors='coerce')
df['Journey_day'] = df['Date_of_Journey'].dt.day
df['Journey_month'] = df['Date_of_Journey'].dt.month
df['Journey_weekday'] = df['Date_of_Journey'].dt.weekday   # Monday=0, Sunday=6

# ===== Departure Time → minutes since midnight =====
df['Dep_Time'] = pd.to_datetime(df['Dep_Time'], format='%H:%M', errors='coerce')
df['Dep_minutes'] = df['Dep_Time'].dt.hour * 60 + df['Dep_Time'].dt.minute

# ===== Arrival Time → minutes since midnight (with next-day correction) =====
def convert_arrival(x):
    try:
        # Remove "Next Day" if present
        if " " in x:
            time_part = x.split(" ")[0]
            next_day = True
        else:
            time_part = x
            next_day = False

        t = pd.to_datetime(time_part, format='%H:%M', errors='coerce')
        if pd.isna(t):
            return np.nan
        minutes = t.hour * 60 + t.minute
        if next_day:
            minutes += 24*60   # ===== add 1440 minutes for next-day arrival =====
        return minutes
    except:
        return np.nan

df['Arrival_minutes'] = df['Arrival_Time'].apply(convert_arrival)

# ===== Duration → total minutes =====
def convert_duration(x):
    try:
        h, m = 0, 0
        if 'h' in x:
            h = int(x.split('h')[0].strip())
            x = x.split('h')[1]
        if 'm' in x:
            m = int(x.split('m')[0].strip())
        return h*60 + m
    except:
        return np.nan

df['Duration_minutes'] = df['Duration'].apply(convert_duration)

# ===== Final Cleanup (Drop Original Columns) =====
df = df.drop(['Date_of_Journey','Dep_Time','Arrival_Time','Duration'], axis=1)

df.head()

# ===== Checking the info of dataset =====
df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 10683 entries, 0 to 10682
Data columns (total 13 columns):
 #   Column            Non-Null Count  Dtype 
---  ------            --------------  ----- 
 0   Airline           10683 non-null  object
 1   Source            10683 non-null  object
 2   Destination       10683 non-null  object
 3   Route             10682 non-null  object
 4   Total_Stops       10682 non-null  object
 5   Additional_Info   10683 non-null  object
 6   Price             10683 non-null  int64 
 7   Journey_day       10683 non-null  int32 
 8   Journey_month     10683 non-null  int32 
 9   Journey_weekday   10683 non-null  int32 
 10  Dep_minutes       10683 non-null  int32 
 11  Arrival_minutes   10683 non-null  int64 
 12  Duration_minutes  10683 non-null  int64 
dtypes: int32(4), int64(3), object(6)
memory usage: 918.2+ KB

# ===== Checking the no. of rows and columns =====
df.shape

(10683, 13)

# ===== Extracting categorical and numerical columns =====
cat_col = [col for col in df.columns if df[col].dtype == 'object']
num_col = [col for col in df.columns if df[col].dtype != 'object']

# ===== Looking at unique values in categorical and numerical columns =====
print("Categorical Columns:\n")
for col in cat_col:
    print(f'\n{col}:\n{df[col].unique()}')

print("\nNumerical Columns:\n")
for col in num_col:
    print(f'\n{col}:\n{df[col].unique()}')

Categorical Columns:


Airline:
['IndiGo' 'Air India' 'Jet Airways' 'SpiceJet' 'Multiple carriers' 'GoAir'
 'Vistara' 'Air Asia' 'Vistara Premium economy' 'Jet Airways Business'
 'Multiple carriers Premium economy' 'Trujet']

Source:
['Banglore' 'Kolkata' 'Delhi' 'Chennai' 'Mumbai']

Destination:
['New Delhi' 'Banglore' 'Cochin' 'Kolkata' 'Delhi' 'Hyderabad']

Route:
['BLR → DEL' 'CCU → IXR → BBI → BLR' 'DEL → LKO → BOM → COK'
 'CCU → NAG → BLR' 'BLR → NAG → DEL' 'CCU → BLR' 'BLR → BOM → DEL'
 'DEL → BOM → COK' 'DEL → BLR → COK' 'MAA → CCU' 'CCU → BOM → BLR'
 'DEL → AMD → BOM → COK' 'DEL → PNQ → COK' 'DEL → CCU → BOM → COK'
 'BLR → COK → DEL' 'DEL → IDR → BOM → COK' 'DEL → LKO → COK'
 'CCU → GAU → DEL → BLR' 'DEL → NAG → BOM → COK' 'CCU → MAA → BLR'
 'DEL → HYD → COK' 'CCU → HYD → BLR' 'DEL → COK' 'CCU → DEL → BLR'
 'BLR → BOM → AMD → DEL' 'BOM → DEL → HYD' 'DEL → MAA → COK' 'BOM → HYD'
 'DEL → BHO → BOM → COK' 'DEL → JAI → BOM → COK' 'DEL → ATQ → BOM → COK'
 'DEL → JDH → BOM → COK' 'CCU → BBI → BOM → BLR' 'BLR → MAA → DEL'
 'DEL → GOI → BOM → COK' 'DEL → BDQ → BOM → COK' 'CCU → JAI → BOM → BLR'
 'CCU → BBI → BLR' 'BLR → HYD → DEL' 'DEL → TRV → COK'
 'CCU → IXR → DEL → BLR' 'DEL → IXU → BOM → COK' 'CCU → IXB → BLR'
 'BLR → BOM → JDH → DEL' 'DEL → UDR → BOM → COK' 'DEL → HYD → MAA → COK'
 'CCU → BOM → COK → BLR' 'BLR → CCU → DEL' 'CCU → BOM → GOI → BLR'
 'DEL → RPR → NAG → BOM → COK' 'DEL → HYD → BOM → COK'
 'CCU → DEL → AMD → BLR' 'CCU → PNQ → BLR' 'BLR → CCU → GAU → DEL'
 'CCU → DEL → COK → BLR' 'BLR → PNQ → DEL' 'BOM → JDH → DEL → HYD'
 'BLR → BOM → BHO → DEL' 'DEL → AMD → COK' 'BLR → LKO → DEL'
 'CCU → GAU → BLR' 'BOM → GOI → HYD' 'CCU → BOM → AMD → BLR'
 'CCU → BBI → IXR → DEL → BLR' 'DEL → DED → BOM → COK'
 'DEL → MAA → BOM → COK' 'BLR → AMD → DEL' 'BLR → VGA → DEL'
 'CCU → JAI → DEL → BLR' 'CCU → AMD → BLR' 'CCU → VNS → DEL → BLR'
 'BLR → BOM → IDR → DEL' 'BLR → BBI → DEL' 'BLR → GOI → DEL'
 'BOM → AMD → ISK → HYD' 'BOM → DED → DEL → HYD' 'DEL → IXC → BOM → COK'
 'CCU → PAT → BLR' 'BLR → CCU → BBI → DEL' 'CCU → BBI → HYD → BLR'
 'BLR → BOM → NAG → DEL' 'BLR → CCU → BBI → HYD → DEL' 'BLR → GAU → DEL'
 'BOM → BHO → DEL → HYD' 'BOM → JLR → HYD' 'BLR → HYD → VGA → DEL'
 'CCU → KNU → BLR' 'CCU → BOM → PNQ → BLR' 'DEL → BBI → COK'
 'BLR → VGA → HYD → DEL' 'BOM → JDH → JAI → DEL → HYD'
 'DEL → GWL → IDR → BOM → COK' 'CCU → RPR → HYD → BLR' 'CCU → VTZ → BLR'
 'CCU → DEL → VGA → BLR' 'BLR → BOM → IDR → GWL → DEL'
 'CCU → DEL → COK → TRV → BLR' 'BOM → COK → MAA → HYD' 'BOM → NDC → HYD'
 'BLR → BDQ → DEL' 'CCU → BOM → TRV → BLR' 'CCU → BOM → HBX → BLR'
 'BOM → BDQ → DEL → HYD' 'BOM → CCU → HYD' 'BLR → TRV → COK → DEL'
 'BLR → IDR → DEL' 'CCU → IXZ → MAA → BLR' 'CCU → GAU → IMF → DEL → BLR'
 'BOM → GOI → PNQ → HYD' 'BOM → BLR → CCU → BBI → HYD' 'BOM → MAA → HYD'
 'BLR → BOM → UDR → DEL' 'BOM → UDR → DEL → HYD' 'BLR → VGA → VTZ → DEL'
 'BLR → HBX → BOM → BHO → DEL' 'CCU → IXA → BLR' 'BOM → RPR → VTZ → HYD'
 'BLR → HBX → BOM → AMD → DEL' 'BOM → IDR → DEL → HYD' 'BOM → BLR → HYD'
 'BLR → STV → DEL' 'CCU → IXB → DEL → BLR' 'BOM → JAI → DEL → HYD'
 'BOM → VNS → DEL → HYD' 'BLR → HBX → BOM → NAG → DEL' nan
 'BLR → BOM → IXC → DEL' 'BLR → CCU → BBI → HYD → VGA → DEL'
 'BOM → BBI → HYD']

Total_Stops:
['non-stop' '2 stops' '1 stop' '3 stops' nan '4 stops']

Additional_Info:
['No info' 'In-flight meal not included' 'No check-in baggage included'
 '1 Short layover' 'No Info' '1 Long layover' 'Change airports'
 'Business class' 'Red-eye flight' '2 Long layover']

Numerical Columns:


Price:
[ 3897  7662 13882 ...  9790 12352 12648]

Journey_day:
[24  1  9 12 27 18  3 15  6 21]

Journey_month:
[3 5 6 4]

Journey_weekday:
[6 2 4 0 1 5 3]

Dep_minutes:
[1340  350  565 1085 1010  540 1135  480  535  685  585 1220  700 1270
 1035 1000  525  840 1215  960  850 1320  240 1285 1310  420  425  590
  875  635  905  855  405 1255  670  345 1140 1385  660  575 1275 1435
 1185  530  940  365  900  835  355  800  305  385 1050  500 1195  390
  845  120  580  505 1225  795  135 1015 1245  315 1190 1200  370 1170
  285  775 1095 1040  925 1380  720  885  710  690  880 1150  360 1410
  455  785  750  910  770 1105  990   40  410  780 1155   90 1020  600
 1175  930  730  970 1235 1345 1265  335  310  400  915   30  510  430
  330  865  325  620 1065  790 1330  295 1070 1280  380  955 1230 1045
  570  450  155  655 1030  550 1125  920 1370  895  860  805 1335  665
  975 1210  415 1145  475  465  610  495  695 1260 1075 1005 1100  230
  515 1160 1205 1060  280 1055  595  300 1080  175 1240 1375 1360 1290
  490 1025  445  945  555  950  705 1325 1115   25 1180 1250 1365  630
 1405  715  645  675  740  870  435   95 1120  560 1315  830  100   20
  255  825 1110  375  125  735  810  395  605  520  185 1295  995  150
  985  340  935  820  440  290  765  625  725  680 1300  180]

Arrival_minutes:
[1510  795 1705 1410 1295  685 2065 1745 1155 1380 1375  835 2000 1190
 2595 2195 1160 2240  410 1310 1935 1655  775  755  560 1395 1260 1220
 1005 1140 1090  915 2580  515 2105  855 2095 1455 1605 2160 1435 1530
 2445 2005  925  935  510  605  870  475  635 1355 1720 2125  445 1245
 2305 1350  800 1400  460 1370 2315  535 1130 1985 1535  580  985 2045
 2110 1025 1070 1390  525 1905  970 1495 2855 1200 1480 2570 1915 1305
 2535  205 2235  255 1270 1265 2025 1085 1850 1320 2355  720  930 1900
  530  480 1175 1415  680  615  765 1580  435  710 2550 1185 2625 1280
 1205  550 2630 1340  610 1500 1430  740 1225 1365 1285  845 1445 1195
 2420  425 1150  725  245 1180 1075 1045 1470 1420 1385 1490 2265 1995
 1235 1870  575  860 1975 1725  630 1165 1775 1980 1360  885  805 1315
 2085  640  780 2770  980 1115 2800 1765 1335  730  735  840 1575  770
 1035  455 1425 1330 2660 1345  745 1835 1520 1125  465  570  265 2590
  260  645 1095 2090 2845 1325 2175 2080  810 2835  815 2815 1055  500
 1105 1990  620 2530  950  690 1405  850 1465 2685  195  955 2705 2820
 1485 1715 2520 2190 1570 1460 1300 2840  520 1015 1110 2185 1230 2795
 2665 1040 1475 1215  750  890  820 2450  865 2010 1080 2165 2075 2345
 1065 2560 2015 1970  190 2440  590 2620 2410 2720  875 1885  785 1060
 2680 2220 1030 1250 2120 1450 1930 2415 2765  965 2040  995 2525 2070
 2540  240 1275  880 1100  975 1545 2430 2155 2030 2260 2055 2360 2545
  430 1210  900 2605  945  760  910 2875 2480  625  790 1240  675  285
 1660 2275  600 2635 2565  960 2135 1965]

Duration_minutes:
[ 170  445 1140  325  285  145  930 1265 1530  470  795  155  135  730
 1595  270 1355 1380 1235  310  920  175  800  910  345  355  805 1320
  330  625  315  150  375  715  665  510 1325  165  720  965 1195  195
 1520  180  975  905  390 1505  745 1640  615  630   90   85 1590  440
  810  300 1145  890  160 1330  575  600 1280 1125  740 1080  555 1050
  995  735  450 1440  535  430  870 1820  900  765  610  925  845 1215
 1390 1090  960  140  480 1015  190  840 1430 1300 1275  650  495  515
  710 1655  505 1255  290  490 1465 1415 1545 1570 1730 1515  560  550
  185  690  570 1055  305 1550 1200  780 1105 1450  295 1535  380 1120
 1165 1760  545  645  700 1375 2245 1540  835  520 1410  755 1455   80
  660  675  875  775  540  460  705 1495 1025 1795 1335  880  435 1210
 1245 1620 1470 1225  335  885  340  245  955  465 1700  260  220  530
 1425 1485 1295  485  385  950 1585 1490 1560 1385  475 1580 1395  320
  240  585  500 1045  425 2045  365  350  420  265  825 1155 1350  985
  830 1625 1690  280  940  275 1110 2295  395  750  680  455 1775 1615
 1420  770  590 1315  655 1270 1240 1800  790  525  370 1065 1305  235
 1040 1830 1285  760 1475 1150 1360  895 1260  405 1720  580 1000  980
 1005   75  415  685  860  725 1445 1695 1070 1220 1685  620  855 2115
 2135 1600 1680  865  785 2240 2170 1555 2105 1185 1675 2820  635   95
  970 2300  360 1010  850 1400 1060  695 1100  400 1855 1480 1790 1705
 1035 1365 1525 1310 1995 1815  215 1660 1825 1130 1665  915  640 1575
 2185 1610  945 1180 1345 1175 1500 1605 2280  255 1510 1095  410 1435
 1075 1405 1030 1460 1710 1630 1160  935  565 1290 2065 1115 1780 1565
 1745 1645  990  670 1735 1750 2040 1840 1845 1975  605 2120 1925 1900
 1190 2025 1810  820 1170 1890 2070 1670 2315 2525  250 2345  230    5
 1950 1915 2000 1650 1135  595 2480 1205 1910 2565  205 2230 1770 1940
 1250 2420  815 2860]

# ===== Count the number of unique values =====
for col in cat_col:
    print(f"Column: '{col}'")
    print(f" * Unique Categories: {df[col].nunique()}")
    print(f" * Category Distribution:\n{df[col].value_counts(dropna=False)}")
    print("-" * 30)

Column: 'Airline'
 * Unique Categories: 12
 * Category Distribution:
Airline
Jet Airways                          3849
IndiGo                               2053
Air India                            1752
Multiple carriers                    1196
SpiceJet                              818
Vistara                               479
Air Asia                              319
GoAir                                 194
Multiple carriers Premium economy      13
Jet Airways Business                    6
Vistara Premium economy                 3
Trujet                                  1
Name: count, dtype: int64
------------------------------
Column: 'Source'
 * Unique Categories: 5
 * Category Distribution:
Source
Delhi       4537
Kolkata     2871
Banglore    2197
Mumbai       697
Chennai      381
Name: count, dtype: int64
------------------------------
Column: 'Destination'
 * Unique Categories: 6
 * Category Distribution:
Destination
Cochin       4537
Banglore     2871
Delhi        1265
New Delhi     932
Hyderabad     697
Kolkata       381
Name: count, dtype: int64
------------------------------
Column: 'Route'
 * Unique Categories: 128
 * Category Distribution:
Route
DEL → BOM → COK                      2376
BLR → DEL                            1552
CCU → BOM → BLR                       979
CCU → BLR                             724
BOM → HYD                             621
                                     ... 
BLR → HBX → BOM → NAG → DEL             1
NaN                                     1
BLR → BOM → IXC → DEL                   1
BLR → CCU → BBI → HYD → VGA → DEL       1
BOM → BBI → HYD                         1
Name: count, Length: 129, dtype: int64
------------------------------
Column: 'Total_Stops'
 * Unique Categories: 5
 * Category Distribution:
Total_Stops
1 stop      5625
non-stop    3491
2 stops     1520
3 stops       45
NaN            1
4 stops        1
Name: count, dtype: int64
------------------------------
Column: 'Additional_Info'
 * Unique Categories: 10
 * Category Distribution:
Additional_Info
No info                         8345
In-flight meal not included     1982
No check-in baggage included     320
1 Long layover                    19
Change airports                    7
Business class                     4
No Info                            3
1 Short layover                    1
Red-eye flight                     1
2 Long layover                     1
Name: count, dtype: int64
------------------------------

# ===== Imputation of categorical features =====
# ===== Drop rare NaN rows in Route and Total_Stops =====
df = df.dropna(subset=['Route', 'Total_Stops'])

# ===== Fix naming issues in Destination =====
df['Destination'] = df['Destination'].replace({'New Delhi': 'Delhi'})

# ===== Fix naming issues in Additional_Info =====
df['Additional_Info'] = df['Additional_Info'].replace({'No Info': 'No info'})

# ===== Check duplicate values =====
# ===== Total number of rows =====
total_rows = len(df)

# ===== Count duplicate rows =====
duplicate_count = df.duplicated().sum()

# ===== Percentage of duplicates =====
duplicate_percentage = (duplicate_count / total_rows) * 100

print(f"Total Rows: {total_rows}")
print(f"Duplicate Rows: {duplicate_count}")
print(f"Percentage of Duplicates: {duplicate_percentage:.2f}%")

Total Rows: 10682
Duplicate Rows: 222
Percentage of Duplicates: 2.08%

# ===== Drop exact duplicates =====
df = df.drop_duplicates()

# ===== Categorical Features =====
# ===== Select categorical columns and exclude 'Route' =====
categorical_cols = df.select_dtypes(include='object').columns
categorical_cols = [col for col in categorical_cols if col != 'Route']

# ===== Subplot grid =====
n_cols = 2
n_rows = (len(categorical_cols) + n_cols - 1) // n_cols
fig, axes = plt.subplots(n_rows, n_cols, figsize=(22, 5*n_rows))
axes = axes.flatten()

# ===== Main title =====
fig.suptitle('Distribution of Categorical Features (Excluding Route)', fontsize=22, fontweight='bold', y=0.98)

# ===== Background color =====
bg_color = '#EDEDED'

# ===== Maroon → Golden Gradient =====
colors_list = ['#FFD700', '#800000']  # Golden → Maroon
custom_cmap = LinearSegmentedColormap.from_list('gold_maroon', colors_list)

# ===== Loop through categorical columns =====
for i, col in enumerate(categorical_cols):
    axes[i].set_facecolor(bg_color)
    axes[i].grid(axis='x', linestyle='--', alpha=0.4, zorder=0)
    axes[i].set_title(f'{col}', fontsize=16, fontweight='bold', color='#222222')
    axes[i].set_xlabel('Count', fontsize=12)

    # ===== All categories sorted ascending for horizontal bars =====
    ctab = df[col].value_counts().sort_values(ascending=True)
    categories = ctab.index
    values = ctab.values

    # ===== Gradient colors proportional to values =====
    norm_values = (values - values.min()) / (values.max() - values.min())
    colors = [custom_cmap(v) for v in norm_values]

    # ===== Horizontal bar plot =====
    bars = axes[i].barh(categories, values, color=colors, edgecolor='#333333', linewidth=0.8, zorder=2)

    # ===== Add counts elegantly =====
    for bar, val in zip(bars, values):
        axes[i].text(val + max(values)*0.01, bar.get_y() + bar.get_height()/2,
                     f"{val}", va='center', fontsize=10, fontweight='bold', color='#222222')

    axes[i].tick_params(axis='y', labelsize=10)

# ===== Remove empty subplots =====
for j in range(i+1, len(axes)):
    fig.delaxes(axes[j])

plt.tight_layout()
plt.subplots_adjust(top=0.92)
plt.show()

# ===== Categorical Features(Route) =====
column_to_plot = 'Route'
top_n = 10
bg_color = '#EDEDED'
colors_list = ['#FFD700', '#800000']  # ===== Golden → Maroon gradient =====
custom_cmap = LinearSegmentedColormap.from_list('gold_maroon', colors_list)

# ===== Prepare data =====
ctab = df[column_to_plot].value_counts()
top_ctab = ctab.nlargest(top_n)
other_count = ctab.iloc[top_n:].sum()

# ===== Combine top categories and 'Other' =====
top_ctab['Other'] = other_count
categories = top_ctab.index
values = top_ctab.values

# ===== Gradient colors proportional to values =====
norm_values = (values - values.min()) / (values.max() - values.min())
colors = [custom_cmap(v) for v in norm_values]

# ===== Plot =====
plt.figure(figsize=(14, 5))
plt.title(f'Distribution of {column_to_plot} (Top {top_n} + Other)', fontsize=20, fontweight='bold', y=1.03)
plt.gca().set_facecolor(bg_color)
plt.grid(axis='x', linestyle='--', alpha=0.4, zorder=0)

# ===== Horizontal bar plot =====
bars = plt.barh(categories, values, color=colors, edgecolor='#333333', linewidth=0.8, zorder=2)

# ===== Add counts at the end of bars =====
for bar, val in zip(bars, values):
    plt.text(val + max(values)*0.01, bar.get_y() + bar.get_height()/2,
             f"{val}", va='center', fontsize=10, fontweight='bold', color='#222222')

# ===== Axis labels =====
plt.xlabel('Count', fontsize=14)
plt.ylabel(column_to_plot, fontsize=14)
plt.yticks(fontsize=10)

plt.tight_layout()
plt.show()

# ===== Distribution of numerical features =====
# ===== Set up =====
plt.style.use('seaborn-v0_8-whitegrid')
sns.set_palette("viridis")

# ===== Select numeric columns =====
numerics = df.select_dtypes(include='number')

# ===== Calculate grid dimensions for subplots - 4 columns per row =====
n_cols = 4
n_rows = (len(numerics.columns) + n_cols - 1) // n_cols

# ===== Create figure with subplots =====
fig, axes = plt.subplots(n_rows, n_cols, figsize=(20, 5*n_rows))
fig.suptitle('Distribution Analysis of Numerical Features',
             fontsize=20, fontweight='bold', y=1.05)

# ===== Flatten axes array for easier indexing =====
axes = axes.flatten()

# ===== Create histplot for each numeric column =====
for i, column in enumerate(numerics.columns):
    # ===== Skip if no more columns =====
    if i >= len(axes):
        break

    # ===== Get data for current column =====
    data = numerics[column].dropna()

    # ===== Create distplot with blue bars and green KDE =====
    sns.histplot(data, kde=True, ax=axes[i], color='#800000',
                 stat='density', alpha=0.7, bins=30)

    # ===== Get KDE line and color it green =====
    # ===== Check if KDE line exists =====
    if axes[i].get_lines():
        kde_line = axes[i].get_lines()[0]
        kde_line.set_color('#FFD700')
        kde_line.set_linewidth(2.5)
        kde_line.set_alpha(0.8)

    # ===== Add statistical information =====
    mean_val = data.mean()
    median_val = data.median()
    skewness = data.skew()
    kurtosis = data.kurtosis()

    # ===== Add vertical lines for mean and median =====
    axes[i].axvline(mean_val, color='blue', linestyle='--', linewidth=2,
                   label=f'Mean: {mean_val:.2f}')
    axes[i].axvline(median_val, color='green', linestyle='--', linewidth=2,
                   label=f'Median: {median_val:.2f}')

    # ===== Set title and labels with enhanced formatting =====
    axes[i].set_title(f'{column}\nSkew: {skewness:.2f} | Kurtosis: {kurtosis:.2f}',
                     fontweight='bold', pad=15)
    axes[i].set_xlabel('Value', fontweight='bold')
    axes[i].set_ylabel('Density', fontweight='bold')

    # ===== Add legend with better positioning =====
    axes[i].legend(loc='upper right', frameon=True, fancybox=True, shadow=True)

    # ===== Add a grid for better readability =====
    axes[i].grid(True, alpha=0.3, linestyle='--')

    # ===== Add a box with summary statistics =====
    textstr = f'n = {len(data):,}\nMin = {data.min():.2f}\nMax = {data.max():.2f}\nσ = {data.std():.2f}'
    props = dict(boxstyle='round', facecolor='lightblue', alpha=0.7, edgecolor='navy')
    axes[i].text(0.02, 0.98, textstr, transform=axes[i].transAxes, fontsize=9,
                verticalalignment='top', bbox=props, fontweight='bold')

    # ===== Set background color for subplot =====
    axes[i].set_facecolor('#f8f9fa')

# ===== Hide any empty subplots =====
for j in range(i+1, len(axes)):
    fig.delaxes(axes[j])

# ===== Adjust layout with better spacing =====
plt.tight_layout()
plt.subplots_adjust(top=0.93, hspace=0.4, wspace=0.3)

# ===== Add a border around the entire figure =====
fig.patch.set_edgecolor('black')
fig.patch.set_linewidth(2)

plt.show()

# ===== Pie Chart Distribution of Categorical Features =====
plt.figure(figsize=(18, 14))
# ===== Clean style with grid =====
plt.style.use('seaborn-v0_8-whitegrid')

# ===== Define a smooth, elegant blue-green palette with accents =====
colors = ['#800000', '#FFD700', '#4B0082', '#FF4500',  '#2E8B57',  '#4682B4', '#DA70D6']

# ===== Select categorical columns =====
categorical_cols = df.select_dtypes(include='object')

for i, col in enumerate(categorical_cols):
    plt.subplot(4, 4, i + 1)

    # ===== Get value counts and handle potential many categories =====
    value_counts = df[col].value_counts(dropna=False)

    # ===== Group small categories into "Other" =====
    if len(value_counts) > 6:
        threshold = 0.05 * value_counts.sum()
        small_categories = value_counts[value_counts < threshold]
        if len(small_categories) > 0:
            value_counts = value_counts[value_counts >= threshold]
            value_counts['Other'] = small_categories.sum()

    labels = [str(x) for x in value_counts.index]
    sizes = value_counts.values

    # ===== Create dynamic colors =====
    n_categories = len(value_counts)
    chart_colors = [colors[j % len(colors)] for j in range(n_categories)]

    # ===== Plot donut chart with percentages inside =====
    wedges, texts, autotexts = plt.pie(
        sizes,
        # ===== Remove labels from outside =====
        labels=None,
        colors=chart_colors,
        autopct='%1.1f%%',
        startangle=90,
        pctdistance=1.1,
        labeldistance=1.2,
        wedgeprops={'edgecolor': 'white', 'linewidth': 2, 'alpha': 0.95},
        textprops={'fontsize': 9, 'weight': 'bold', 'color': 'black'}
    )

    # ===== Style percentages =====
    for autotext in autotexts:
        autotext.set_weight('bold')
        autotext.set_fontsize(10)

    # ===== Donut effect =====
    centre_circle = plt.Circle((0, 0), 0.60, fc='white')
    plt.gca().add_artist(centre_circle)

    # ===== Add legend instead of labels outside =====
    plt.legend(wedges, labels, title=col.title(), loc="center left", bbox_to_anchor=(1, 0, 0.5, 1))

    # ===== Keep it circular =====
    plt.axis('equal')
    plt.title(col.title(), fontsize=12, weight='bold', pad=15)

plt.suptitle('Distribution of Categorical Variables', fontsize=20, weight='bold', y=0.98)
plt.tight_layout(rect=[0, 0.03, 1, 0.95])
plt.show()

# ===== Regression plot of feature vs Target Variable =====
# ===== gray background =====
sns.set_theme(style="darkgrid")

# ===== Select numeric columns =====
numerics = df.select_dtypes(include='number').columns.tolist()

# ===== Define target column (Price) =====
target_col = 'Price'

# Remove target from feature list
if target_col in numerics:
    numerics.remove(target_col)

# ===== Copy numeric features and target column =====
numeric_df_copied = df[numerics + [target_col]].copy()

# ===== Drop missing values =====
numeric_df_copied = numeric_df_copied.dropna()

# ===== Sample data for faster plotting =====
if len(numeric_df_copied) > 5000:
    numeric_df_copied = numeric_df_copied.sample(5000, random_state=42)

# ===== Setup subplots =====
n_cols = 4
n_rows = int(np.ceil(len(numerics) / n_cols))

fig, axes = plt.subplots(n_rows, n_cols, figsize=(22, 18))
axes = axes.flatten()

fig.suptitle('Regression Plots: Numeric Features vs Flight Price',
             fontsize=24, fontweight='bold', y=0.98)

for i, column in enumerate(numerics):
    ax = axes[i]

    # ===== Scatter + Regression line =====
    sns.regplot(
        data=numeric_df_copied,
        x=column,
        y=target_col,
        scatter_kws={'alpha':0.5, 's':30, 'color':'#FFD700', 'edgecolor':'white'},
        line_kws={'color':'#800000', 'linewidth':2},
        ci=95,
        ax=ax
    )

    # ===== Customize =====
    ax.set_title(column.title(), fontsize=14, fontweight='bold')
    ax.set_xlabel(column.title(), fontsize=12, fontweight='bold')
    ax.set_ylabel('Flight Price (₹)', fontsize=12, fontweight='bold')
    ax.grid(True, alpha=0.5)

# ===== Remove empty subplots if extra =====
for j in range(i+1, len(axes)):
    fig.delaxes(axes[j])

plt.tight_layout(rect=[0, 0, 1, 0.96])
plt.show()

# ===== Visualization code =====
# ===== Bin Price into categories =====
df_air = df.copy()
bins = [0, 5000, 10000, 15000, 20000, df_air['Price'].max()]
labels = ['0-5k', '5k-10k', '10k-15k', '15k-20k', '20k+']
df_air['Price_Range'] = pd.cut(df_air['Price'], bins=bins, labels=labels)

plt.figure(figsize=(20,10))
sns.countplot(
    data=df_air,
    x='Airline',
    hue='Price_Range',
    palette=['#800000', '#FFD700', 'red', 'navy', 'green'],
    edgecolor='black'
)

plt.title("Airline Segmentation by Price Ranges", fontsize=18, weight='bold')
plt.xlabel("Airline", fontsize=12)
plt.ylabel("Count", fontsize=12)
plt.xticks(rotation=45, fontsize=10)
plt.yticks(fontsize=10)
plt.legend(title='Price Range (INR)', title_fontsize=12, fontsize=10, loc='upper right')
plt.grid(axis='y', linestyle='--', alpha=0.4)

plt.tight_layout()
plt.show()

# ===== Figure settings =====
plt.figure(figsize=(20, 10))
ax = plt.gca()

# ===== Sort airlines by median price for better visual =====
airline_order = df.groupby('Airline')['Price'].median().sort_values().index

colors = np.linspace(0, 1, len(df['Airline'].unique()))
cmap = LinearSegmentedColormap.from_list("maroon_gold", ["#FFD700", "#800000"])
bar_colors = [cmap(val) for val in colors]

sns.barplot(
    x='Airline',
    y='Price',
    data=df,
    order=airline_order,
    palette=bar_colors,
    edgecolor='black',
    ci=None
)

ax.set_facecolor('#EDEDED')
ax.grid(axis='y', linestyle='-', alpha=0.2)
plt.title('Airline vs Price', fontsize=24, weight='bold', color='#222222')
plt.xlabel('Airline', fontsize=18, weight='bold', color='#333333')
plt.ylabel('Price (INR)', fontsize=18, weight='bold', color='#333333')
plt.xticks(rotation=45, ha='right', fontsize=12, weight='bold', color='#222222')
plt.yticks(fontsize=12, weight='bold', color='#222222')

plt.tight_layout()
plt.show()

# ===== Select categorical columns excluding 'Route' and 'Airline' =====
categorical_cols = df.select_dtypes(include='object').columns
categorical_cols = [col for col in categorical_cols if col not in ['Route', 'Airline']]

# ===== Figure settings =====
n_cols = 2
n_rows = (len(categorical_cols) + n_cols - 1) // n_cols
fig, axes = plt.subplots(n_rows, n_cols, figsize=(20, 5*n_rows))
axes = axes.flatten()

# ===== Loop through categorical columns =====
for i, col in enumerate(categorical_cols):
    ax = axes[i]
    # ===== Boxplot =====
    sns.boxplot(
        x=col,
        y='Price',
        data=df,
        ax=ax,
        boxprops=dict(facecolor='#FFD700', color='black', linewidth=1.2),
        whiskerprops=dict(color='black', linewidth=1),
        capprops=dict(color='black', linewidth=1),
        medianprops=dict(color='#800000', linewidth=2),
        flierprops=dict(marker='o', markerfacecolor='#800000', markersize=5, alpha=0.8, markeredgecolor='black')
    )

    ax.set_title(f'{col} vs Price', fontsize=16, weight='bold', color='#222222')
    ax.set_xlabel(col, fontsize=12, weight='bold', color='#333333')
    ax.set_ylabel('Price (INR)', fontsize=12, weight='bold', color='#333333')
    ax.tick_params(axis='x', rotation=45, labelsize=10)
    ax.grid(axis='y', linestyle='--', alpha=0.3)

for j in range(i+1, len(axes)):
    fig.delaxes(axes[j])

plt.tight_layout()
plt.suptitle('Categorical Features vs Price', fontsize=20, weight='bold', y=1.05)
plt.show()

# ===== Correlation Heatmap visualization code =====
numeric_df = df.select_dtypes(include=['number'])

custom_cmap = sns.color_palette("blend:#FFD700,white,#800000", as_cmap=True)

plt.figure(figsize=(15,6))
sns.heatmap(
    numeric_df.corr(),
    annot=True,
    fmt=".2f",
    cmap=custom_cmap,
    center=0,
    linewidths=1.5,
    linecolor="lightgrey",
    annot_kws={"size":12, "weight":"bold", "color":"black"},
    cbar_kws={"shrink":0.7, "aspect":30, "label":"Correlation Strength"}
)

plt.title("Correlation Heatmap of Numeric Features",
          fontsize=16, fontweight="bold", color="black", pad=20)
plt.xticks(rotation=45, ha="right", fontsize=11, weight="bold", color="#222")
plt.yticks(rotation=0, fontsize=11, weight="bold", color="#222")
plt.grid(False)
plt.tight_layout()
plt.show()

# ===== Stacked Bar Chart – Airline vs Source vs Price   =====
# === Prepare grouped data ===
route_airline = df.groupby(["Airline", "Source"])["Price"].count().unstack().fillna(0)

# ===== Convert counts to percentages =====
route_airline_pct = route_airline.div(route_airline.sum(axis=1), axis=0) * 100

# === Define custom color palette for Sources ===
custom_colors = {
    "Banglore": "gold",
    "Chennai": "navy",
    "Delhi": "maroon",
    "Kolkata": "purple",
    "Mumbai": "green"
}

colors = [custom_colors.get(col, "gray") for col in route_airline_pct.columns]
fig, ax = plt.subplots(figsize=(20,9))
route_airline_pct.plot(
    kind="barh",
    stacked=True,
    color=colors,
    edgecolor="black",
    linewidth=0.7,
    ax=ax
)

# Title & Labels
plt.title("Airline vs Source – Flight Distribution", fontsize=22, weight="bold", color="#222831", pad=20)
plt.xlabel("Percentage of Flights (%)", fontsize=16, weight="bold", color="#393E46", labelpad=15)
plt.ylabel("Airline", fontsize=16, weight="bold", color="#393E46", labelpad=15)

# Y-axis ticks
plt.yticks(fontsize=12, weight="bold", color="#222831")

# X-axis ticks
plt.xticks(fontsize=12, weight="bold", color="#222831")

# Grid only on x-axis
plt.grid(axis="x", linestyle="--", alpha=0.4)

# Legend styling (bottom left, outside plot area)
legend = plt.legend(
    title="Source",
    fontsize=12,
    title_fontsize=13,
    loc="lower left",
    bbox_to_anchor=(-0.19, -0.03),
    frameon=True,
    shadow=True,
    fancybox=True,
    borderpad=1
)
plt.setp(legend.get_title(), weight="bold")

# === Annotate percentages inside bars (skip 0%) ===
for container in ax.containers:
    labels = [f"{w:.1f}%" if w > 0 else "" for w in container.datavalues]
    ax.bar_label(container, labels=labels, label_type="center", fontsize=10, weight="bold", color="black")

plt.tight_layout()
plt.show()

# ===== Pair Plot visualization code =====
numeric_df = df.select_dtypes(include=['number'])

sns.pairplot(numeric_df, plot_kws={"color": "maroon"}, diag_kws={"color": "#FFD700"})
plt.show()

# ===== Create contingency table =====
# ===== Group prices by Airline =====
groups = [df[df['Airline'] == airline]['Price'] for airline in df['Airline'].unique()]

# ===== Perform ANOVA =====
f_stat, p_val = f_oneway(*groups)

print("Airline vs Price - ANOVA Test\n")
print("F-statistic:", f_stat)
print("P-value:", p_val)

# ===== Interpretation =====
if p_val < 0.05:
    print("\nResult: Reject H0 → Airline has a significant impact on flight price.")
else:
    print("\nResult: Fail to Reject H0 → No significant difference across Airlines.")

Airline vs Price - ANOVA Test

F-statistic: 654.1998364047217
P-value: 0.0

Result: Reject H0 → Airline has a significant impact on flight price.

# ===== Create contingency table =====
# ===== Group prices by Total Stops =====
groups = [df[df['Total_Stops'] == stop]['Price'] for stop in df['Total_Stops'].unique()]

# ===== Perform ANOVA =====
f_stat, p_val = f_oneway(*groups)

print("Total_Stops vs Price - ANOVA Test\n")
print("F-statistic:", f_stat)
print("P-value:", p_val)

# ===== Interpretation =====
if p_val < 0.05:
    print("\nResult: Reject H0 → Number of stops significantly affects flight price.")
else:
    print("\nResult: Fail to Reject H0 → Stops do not significantly affect flight price.")

Total_Stops vs Price - ANOVA Test

F-statistic: 1722.028490860059
P-value: 0.0

Result: Reject H0 → Number of stops significantly affects flight price.

# ===== Create contingency table =====
# ===== Perform Pearson Correlation =====
corr, p_val = pearsonr(df['Duration_minutes'], df['Price'])

print("\nDuration vs Price - Correlation Test\n")
print("Correlation Coefficient:", corr)
print("P-value:", p_val)

# ===== Interpretation =====
if p_val < 0.05:
    print("\nResult: Reject H0 → Flight duration is significantly correlated with Price.")
else:
    print("\nResult: Fail to Reject H0 → No significant correlation between Duration and Price.")

Duration vs Price - Correlation Test

Correlation Coefficient: 0.5017099519431807
P-value: 0.0

Result: Reject H0 → Flight duration is significantly correlated with Price.

# ===== Finding a missing values =====
df.isnull().sum().to_frame("Missing_Values")

# ===== Plotting box plots for all numerical variable =====
numeric_df = df.select_dtypes(include=['number'])

# ===== Background =====
plt.style.use('ggplot')

plt.figure(figsize=(20, 15))
num_plots = min(len(numeric_df.columns), 13)

for i, col in enumerate(numeric_df.columns[:num_plots]):
    plt.subplot(4, 4, i + 1)

    sns.boxplot(
        data=df,
        x=col,
        boxprops=dict(color='#FFD700', facecolor='#800000', linewidth=3),
        flierprops=dict(marker='o', markerfacecolor='#800000', markersize=5, linestyle='none'),
        medianprops=dict(color='#800000', linewidth=2),
        whiskerprops=dict(color='#FFD700', linewidth=3),
        capprops=dict(color='#FFD700', linewidth=3)
    )

    plt.title(col, fontsize=12, fontweight='bold')
    plt.xlabel('')

plt.suptitle("Outlier Visualization in Numerical Columns", fontsize=20, fontweight='bold', y=1.02)
plt.tight_layout()
plt.show()

# ===== Defining the function for outlier detection and percentage calculation using IQR =====

def detect_outliers(data):
    data = np.array(data)

    # ===== Quartiles =====
    q1 = np.percentile(data, 25)
    q2 = np.percentile(data, 50)
    q3 = np.percentile(data, 75)

    # ===== IQR & boundsa =====
    IQR = q3 - q1
    lower_bound = q1 - 1.5 * IQR
    upper_bound = q3 + 1.5 * IQR

    # ===== Outlier detection =====
    outliers = data[(data < lower_bound) | (data > upper_bound)]
    outlier_count = len(outliers)
    outlier_percent = round(outlier_count * 100 / len(data), 2)

    # ===== Display results =====
    print(f"Q1 = {q1}, Q2 (Median) = {q2:.2f}, Q3 = {q3}")
    print(f"IQR = {IQR:.2f}")
    print(f"Lower Bound = {lower_bound:.2f}, Upper Bound = {upper_bound:.2f}")
    print(f"Outliers Detected: {outlier_count}")
    print(f"Outlier Percentage: {outlier_percent}%\n")

# ===== Calculating IQR, Lower/Upper Bounds, and Outlier Counts for Continuous Numerical Features =====

for feature in numeric_df:
  print(feature,":")
  detect_outliers(df[feature])
  print("*"*50)

Price :
Q1 = 5224.0, Q2 (Median) = 8266.00, Q3 = 12346.25
IQR = 7122.25
Lower Bound = -5459.38, Upper Bound = 23029.62
Outliers Detected: 94
Outlier Percentage: 0.9%

**************************************************
Journey_day :
Q1 = 6.0, Q2 (Median) = 12.00, Q3 = 21.0
IQR = 15.00
Lower Bound = -16.50, Upper Bound = 43.50
Outliers Detected: 0
Outlier Percentage: 0.0%

**************************************************
Journey_month :
Q1 = 3.0, Q2 (Median) = 5.00, Q3 = 6.0
IQR = 3.00
Lower Bound = -1.50, Upper Bound = 10.50
Outliers Detected: 0
Outlier Percentage: 0.0%

**************************************************
Journey_weekday :
Q1 = 1.0, Q2 (Median) = 3.00, Q3 = 5.0
IQR = 4.00
Lower Bound = -5.00, Upper Bound = 11.00
Outliers Detected: 0
Outlier Percentage: 0.0%

**************************************************
Dep_minutes :
Q1 = 480.0, Q2 (Median) = 705.00, Q3 = 1080.0
IQR = 600.00
Lower Bound = -420.00, Upper Bound = 1980.00
Outliers Detected: 0
Outlier Percentage: 0.0%

**************************************************
Arrival_minutes :
Q1 = 980.0, Q2 (Median) = 1305.00, Q3 = 1720.0
IQR = 740.00
Lower Bound = -130.00, Upper Bound = 2830.00
Outliers Detected: 56
Outlier Percentage: 0.54%

**************************************************
Duration_minutes :
Q1 = 170.0, Q2 (Median) = 505.00, Q3 = 910.0
IQR = 740.00
Lower Bound = -940.00, Upper Bound = 2020.00
Outliers Detected: 75
Outlier Percentage: 0.72%

**************************************************

# ===== Defining the function for outlier removal code =====

def remove_outliers_iqr(df, column):
    Q1 = df[column].quantile(0.25)
    Q3 = df[column].quantile(0.75)
    IQR = Q3 - Q1
    lower_bound = Q1 - 1.5 * IQR
    upper_bound = Q3 + 1.5 * IQR

    filtered_df = df[(df[column] >= lower_bound) & (df[column] <= upper_bound)]
    print(f"Removed {df.shape[0] - filtered_df.shape[0]} outliers from '{column}'")
    return filtered_df

# ===== Run code =====
# ===== copy for camparison purposs =====
df_clean = df.copy()

df_clean = remove_outliers_iqr(df_clean, 'Price')
df_clean = remove_outliers_iqr(df_clean, 'Duration_minutes')

Removed 94 outliers from 'Price'
Removed 74 outliers from 'Duration_minutes'

# ===== Boxplot comparison code =====

box_style = dict(
    boxprops=dict(color='#FFD700', facecolor='#FFD700', linewidth=3),
    flierprops=dict(marker='o', markerfacecolor='#800000', markersize=5, linestyle='none'),
    medianprops=dict(color='#800000', linewidth=2),
    whiskerprops=dict(color='#FFD700', linewidth=3),
    capprops=dict(color='#FFD700', linewidth=3)
)

columns_to_plot = ['Price', 'Duration_minutes']
titles = ['Price', 'Duration_minutes']

fig, axes = plt.subplots(2, 1, figsize=(15, 7))

for i, col in enumerate(columns_to_plot):
    combined_data = pd.concat([df[col], df_clean[col]])
    group_labels = ['Before'] * len(df[col]) + ['After'] * len(df_clean[col])

    sns.boxplot(
        y=group_labels,
        x=combined_data,
        ax=axes[i],
        color='white',
        **box_style
    )

    axes[i].set_title(f'{titles[i]} (Before vs After)', fontsize=16, fontweight='bold')
    axes[i].set_xlabel('')
    axes[i].set_ylabel('')
    axes[i].grid(True, axis='x', linestyle='--', alpha=0.5)

    axes[i].set_yticklabels(['Before', 'After'], fontsize=14, weight='bold')
    for tick in axes[i].get_yticklabels():
        if tick.get_text() == 'Before':
            tick.set_color('crimson')
        elif tick.get_text() == 'After':
            tick.set_color('darkgreen')

plt.suptitle('Boxplot Comparison', fontsize=20, fontweight='bold', color='navy')
plt.tight_layout(rect=[0, 0.03, 1, 0.95])
plt.show()

# ===== After comparing box plots, I made the following changes =====

df = df_clean.copy()

# ===== Categorical Features =====
# ===== Run code =====
categorical_cols = df.select_dtypes(include='object')
for col in categorical_cols:
    print(f"Column: '{col}'")
    print(f" * Unique Categories: {df[col].nunique()}")
    print(f" * Category Distribution:\n{df[col].value_counts(dropna=False)}")
    print("-" * 35)

Column: 'Airline'
 * Unique Categories: 11
 * Category Distribution:
Airline
Jet Airways                          3613
IndiGo                               2043
Air India                            1630
Multiple carriers                    1186
SpiceJet                              814
Vistara                               477
Air Asia                              318
GoAir                                 194
Multiple carriers Premium economy      13
Vistara Premium economy                 3
Trujet                                  1
Name: count, dtype: int64
-----------------------------------
Column: 'Source'
 * Unique Categories: 5
 * Category Distribution:
Source
Delhi       4271
Kolkata     2853
Banglore    2097
Mumbai       690
Chennai      381
Name: count, dtype: int64
-----------------------------------
Column: 'Destination'
 * Unique Categories: 5
 * Category Distribution:
Destination
Cochin       4271
Banglore     2853
Delhi        2097
Hyderabad     690
Kolkata       381
Name: count, dtype: int64
-----------------------------------
Column: 'Route'
 * Unique Categories: 125
 * Category Distribution:
Route
DEL → BOM → COK                      2368
BLR → DEL                            1532
CCU → BOM → BLR                       979
CCU → BLR                             723
BOM → HYD                             621
                                     ... 
BOM → JAI → DEL → HYD                   1
BLR → HBX → BOM → NAG → DEL             1
BLR → BOM → IXC → DEL                   1
BLR → CCU → BBI → HYD → VGA → DEL       1
BOM → BBI → HYD                         1
Name: count, Length: 125, dtype: int64
-----------------------------------
Column: 'Total_Stops'
 * Unique Categories: 5
 * Category Distribution:
Total_Stops
1 stop      5550
non-stop    3470
2 stops     1242
3 stops       29
4 stops        1
Name: count, dtype: int64
-----------------------------------
Column: 'Additional_Info'
 * Unique Categories: 6
 * Category Distribution:
Additional_Info
No info                         8040
In-flight meal not included     1918
No check-in baggage included     318
1 Long layover                     9
Change airports                    6
Red-eye flight                     1
Name: count, dtype: int64
-----------------------------------

# ===== Encode the categorical features =====
# ===== Define Feature Groups =====
one_hot_features = ["Airline", "Source", "Destination", "Additional_Info"]
ordinal_features = ["Total_Stops"]
frequency_features = ['Route']

# Ordinal mapping for Total_Stops
ordinal_mapping = [['non-stop', '1 stop', '2 stops', '3 stops', '4 stops']]

# ===== Build Encoding Pipeline =====
preprocessor = ColumnTransformer(
    transformers=[
        ("onehot", OneHotEncoder(drop="first"), one_hot_features),
        ("ordinal", OrdinalEncoder(categories=ordinal_mapping), ordinal_features),
        ("freq", CountEncoder(), frequency_features)
    ],
    # ===== keep numeric + binary features =====
    remainder="passthrough"
)

# ===== Fit & Transform =====
df_fit = preprocessor.fit_transform(df)

# ===== Get Feature Names =====
onehot_feature_names = preprocessor.named_transformers_["onehot"].get_feature_names_out(one_hot_features)
ordinal_feature_names = ordinal_features
frequency_features_names = frequency_features
passthrough_features = [col for col in df.columns if col not in one_hot_features + ordinal_features + frequency_features]

# Final feature names
final_feature_names = list(onehot_feature_names) + ordinal_feature_names + frequency_features_names + passthrough_features

# ===== Convert to DataFrame =====
df_encoded = pd.DataFrame(df_fit, columns=final_feature_names, index=df.index)

# ===== Convert all boolean columns to integers =====
bool_cols = df_encoded.select_dtypes(include='bool').columns
df_encoded[bool_cols] = df_encoded[bool_cols].astype(int)

# ===== Final Output =====
print("Shape of encoded dataset:", df_encoded.shape)
print(df_encoded.head())

Shape of encoded dataset: (10292, 32)
   Airline_Air India  Airline_GoAir  Airline_IndiGo  Airline_Jet Airways  \
0                0.0            0.0             1.0                  0.0   
1                1.0            0.0             0.0                  0.0   
2                0.0            0.0             0.0                  1.0   
3                0.0            0.0             1.0                  0.0   
4                0.0            0.0             1.0                  0.0   

   Airline_Multiple carriers  Airline_Multiple carriers Premium economy  \
0                        0.0                                        0.0   
1                        0.0                                        0.0   
2                        0.0                                        0.0   
3                        0.0                                        0.0   
4                        0.0                                        0.0   

   Airline_SpiceJet  Airline_Trujet  Airline_Vistara  \
0               0.0             0.0              0.0   
1               0.0             0.0              0.0   
2               0.0             0.0              0.0   
3               0.0             0.0              0.0   
4               0.0             0.0              0.0   

   Airline_Vistara Premium economy  ...  Additional_Info_Red-eye flight  \
0                              0.0  ...                             0.0   
1                              0.0  ...                             0.0   
2                              0.0  ...                             0.0   
3                              0.0  ...                             0.0   
4                              0.0  ...                             0.0   

   Total_Stops   Route    Price  Journey_day  Journey_month  Journey_weekday  \
0          0.0  1532.0   3897.0         24.0            3.0              6.0   
1          2.0     6.0   7662.0          1.0            5.0              2.0   
2          2.0    41.0  13882.0          9.0            6.0              6.0   
3          1.0     9.0   6218.0         12.0            5.0              6.0   
4          1.0     3.0  13302.0          1.0            3.0              4.0   

   Dep_minutes  Arrival_minutes  Duration_minutes  
0       1340.0           1510.0             170.0  
1        350.0            795.0             445.0  
2        565.0           1705.0            1140.0  
3       1085.0           1410.0             325.0  
4       1010.0           1295.0             285.0  

[5 rows x 32 columns]

# ===== Checking =====
df_encoded.tail(10).T

# ===== Select your features wisely to avoid overfitting =====
# ===== Correlation Heatmap visualization code =====

corr = df_encoded.corr(numeric_only=True)
top_features = corr.abs().nlargest(10, 'Price').index
top_corr = df_encoded[top_features].corr()

custom_cmap = sns.color_palette("blend:#FFD700,white,#800000", as_cmap=True)

plt.figure(figsize=(15,6))
sns.heatmap(
    top_corr,
    annot=True,
    fmt=".2f",
    cmap=custom_cmap,
    center=0,
    linewidths=1.5,
    linecolor="lightgrey",
    annot_kws={"size":12, "weight":"bold", "color":"black"},
    cbar_kws={"shrink":0.7, "aspect":30, "label":"Correlation Strength"}
)

plt.title("Top Feature Correlations",
          fontsize=16, fontweight="bold", color="black", pad=20)
plt.xticks(rotation=45, ha="right", fontsize=11, weight="bold", color="#222")
plt.yticks(rotation=0, fontsize=11, weight="bold", color="#222")
plt.grid(False)
plt.tight_layout()
plt.show()

# ===== Defining a function for variance_inflation_factor =====

def calc_vif(df):
    """
    Calculates Variance Inflation Factor (VIF) for each numerical feature in the dataframe.

    Parameters:
        df (pd.DataFrame): Input dataframe with features

    Returns:
        pd.DataFrame: VIF values sorted in descending order
    """
    # ===== Select only numeric columns =====
    X = df.select_dtypes(include=[np.number])

    # ===== Add constant to the model for intercept =====
    X = add_constant(X)

    # ===== Compute VIF for each feature =====
    vif_data = pd.DataFrame()
    vif_data["Feature"] = X.columns
    vif_data["VIF"] = [variance_inflation_factor(X.values, i) for i in range(X.shape[1])]

    # ===== Drop the constant term and sort results =====
    vif_data = vif_data[vif_data["Feature"] != "const"]
    return vif_data.sort_values(by="VIF", ascending=False).reset_index(drop=True)

# ===== Run code =====
df_encoded_vif = df_encoded.drop("Price", axis=1).copy()
vif_result = calc_vif(df_encoded_vif)
print(vif_result)

                                         Feature         VIF
0                                 Source_Kolkata         inf
1                                  Source_Mumbai         inf
2                             Destination_Cochin         inf
3                                   Source_Delhi         inf
4                                 Source_Chennai         inf
5                          Destination_Hyderabad         inf
6                              Destination_Delhi         inf
7                            Destination_Kolkata         inf
8                        Additional_Info_No info  197.207779
9    Additional_Info_In-flight meal not included  176.318554
10                               Arrival_minutes   77.797906
11                              Duration_minutes   52.058923
12  Additional_Info_No check-in baggage included   36.026966
13                                   Dep_minutes   26.214838
14                           Airline_Jet Airways    9.309516
15                                Airline_IndiGo    6.111731
16                             Airline_Air India    5.627517
17                     Airline_Multiple carriers    5.016531
18                              Airline_SpiceJet    3.957277
19                                   Total_Stops    3.721193
20                               Airline_Vistara    2.458753
21                                         Route    2.021528
22               Additional_Info_Change airports    1.673063
23                                 Airline_GoAir    1.613533
24                Additional_Info_Red-eye flight    1.115270
25                                 Journey_month    1.103272
26     Airline_Multiple carriers Premium economy    1.058257
27                                   Journey_day    1.033295
28                               Journey_weekday    1.019019
29               Airline_Vistara Premium economy    1.011878
30                                Airline_Trujet    1.005676

# ===== Checking =====
df_encoded.columns

Index(['Airline_Air India', 'Airline_GoAir', 'Airline_IndiGo',
       'Airline_Jet Airways', 'Airline_Multiple carriers',
       'Airline_Multiple carriers Premium economy', 'Airline_SpiceJet',
       'Airline_Trujet', 'Airline_Vistara', 'Airline_Vistara Premium economy',
       'Source_Chennai', 'Source_Delhi', 'Source_Kolkata', 'Source_Mumbai',
       'Destination_Cochin', 'Destination_Delhi', 'Destination_Hyderabad',
       'Destination_Kolkata', 'Additional_Info_Change airports',
       'Additional_Info_In-flight meal not included',
       'Additional_Info_No check-in baggage included',
       'Additional_Info_No info', 'Additional_Info_Red-eye flight',
       'Total_Stops', 'Route', 'Price', 'Journey_day', 'Journey_month',
       'Journey_weekday', 'Dep_minutes', 'Arrival_minutes',
       'Duration_minutes'],
      dtype='object')

# ===== Creating final dataframe considering above selected features =====
final_df= df_encoded[['Airline_Air India', 'Airline_GoAir', 'Airline_IndiGo', 'Airline_Jet Airways', 'Airline_Multiple carriers', 'Airline_Multiple carriers Premium economy',
                      'Airline_SpiceJet', 'Airline_Trujet', 'Airline_Vistara', 'Airline_Vistara Premium economy', 'Route', 'Total_Stops', 'Journey_day', 'Journey_month',
                      'Journey_weekday', 'Arrival_minutes', 'Duration_minutes', 'Price']]

# ===== Check a final dataset =====

final_df.head().T

# ===== checking which of the variables are continous in nature =====

for i in final_df.columns:
  print(f"The number of unique counts in feature {i} is: {final_df[i].nunique()}")

The number of unique counts in feature Airline_Air India is: 2
The number of unique counts in feature Airline_GoAir is: 2
The number of unique counts in feature Airline_IndiGo is: 2
The number of unique counts in feature Airline_Jet Airways is: 2
The number of unique counts in feature Airline_Multiple carriers is: 2
The number of unique counts in feature Airline_Multiple carriers Premium economy is: 2
The number of unique counts in feature Airline_SpiceJet is: 2
The number of unique counts in feature Airline_Trujet is: 2
The number of unique counts in feature Airline_Vistara is: 2
The number of unique counts in feature Airline_Vistara Premium economy is: 2
The number of unique counts in feature Route is: 54
The number of unique counts in feature Total_Stops is: 5
The number of unique counts in feature Journey_day is: 10
The number of unique counts in feature Journey_month is: 4
The number of unique counts in feature Journey_weekday is: 7
The number of unique counts in feature Arrival_minutes is: 301
The number of unique counts in feature Duration_minutes is: 343
The number of unique counts in feature Price is: 1805

# ===== Checking the distribution and Q-Q plot of each continous variable from our final dataframe =====

# ===== Define continuous features to analyze =====
selected_features = ['Arrival_minutes', 'Duration_minutes', 'Price']

# ===== Check skewness =====
print("Skewness Before Transformation:")
for col in selected_features:
    skew_val = round(final_df[col].skew(), 2)
    print(f"  {col}: {skew_val}")

# ===== Set theme =====
sns.set_style("darkgrid")

# ===== Plot Distribution + Q-Q side by side for each feature =====
for col in selected_features:
    fig, axes = plt.subplots(1, 2, figsize=(14, 4.5))

    # ===== Distribution plot (left) =====
    sns.histplot(final_df[col], kde=True, color='#FFD700', ax=axes[0])
    axes[0].set_title(f'Distribution of {col}')

    # ===== Q-Q plot (right) =====
    stats.probplot(final_df[col], dist="norm", plot=axes[1])
    axes[1].set_title(f'Q-Q Plot of {col}')

    # ===== Overall title for this feature only =====
    fig.suptitle(f"Analysis of {col}", fontsize=16, fontweight="bold", color="black", y=1.02)

    plt.tight_layout()
    plt.show()

Skewness Before Transformation:
  Arrival_minutes: 0.46
  Duration_minutes: 0.81
  Price: 0.45

# ===== Applying Square root transformation on the above considered columns =====

# ===== Apply Square Root Transformation =====
final_df['Duration_minutes'] = np.sqrt(final_df['Duration_minutes'])

print("After Applying Square Root Transformation")
print("Skewness:")
print(f" - Duration_minutes: {round(final_df['Duration_minutes'].skew(), 2)}")

# ===== Set theme =====
sns.set_style("darkgrid")

# ===== Create figure with 1 row, 2 columns =====
fig, axes = plt.subplots(1, 2, figsize=(14, 4))

# --- Left: Distribution plot ---
sns.histplot(final_df['Duration_minutes'], kde=True, bins=30, color='#FFD700', ax=axes[0])
axes[0].set_title("Distribution of Duration_minutes (After Square Root Transformation)")

# --- Right: Q-Q plot ---
stats.probplot(final_df['Duration_minutes'], dist="norm", plot=axes[1])
axes[1].set_title("Q-Q Plot of Duration_minutes (After Square Root Transformation)")

# ===== Add overall title for this pair =====
fig.suptitle(f"Analysis of Duration_minutes", fontsize=16, fontweight="bold", color="black", y=1.02)

plt.tight_layout()
plt.show()

After Applying Square Root Transformation
Skewness:
 - Duration_minutes: 0.34

# ===== Applying StandardScaler for Feature Normalization =====

final_scale_df = final_df.copy()

scaler = StandardScaler()
final_scale_df[['Arrival_minutes', 'Duration_minutes']] = scaler.fit_transform(final_scale_df[['Arrival_minutes', 'Duration_minutes']])

# ===== Split your data to train and test. Choose Splitting ratio wisely =====
x= final_scale_df.drop(columns='Price',axis=1)
y= final_scale_df[['Price']]

# ===== Spliting data =====
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2, random_state=0)

# ===== Checking the distribution of classes in training and testing sets =====
# ===== Dataset Split Summary =====
split_summary = pd.DataFrame({
    "Dataset": ["x_train", "x_test", "y_train", "y_test"],
    "Shape": [x_train.shape, x_test.shape, y_train.shape, y_test.shape]
})

print("Dataset Split Summary\n")
print(split_summary.to_string(index=False))
print("-" * 36)

# ===== Target Variable Summary Statistics =====
y_train_stats = y_train.describe()
y_test_stats = y_test.describe()

target_summary = pd.concat([y_train_stats, y_test_stats], axis=1)
target_summary.columns = ["Train Summary", "Test Summary"]

print("\nTarget Variable Summary Statistics\n")
print(target_summary)

Dataset Split Summary

Dataset      Shape
x_train (8233, 17)
 x_test (2059, 17)
y_train  (8233, 1)
 y_test  (2059, 1)
------------------------------------

Target Variable Summary Statistics

       Train Summary  Test Summary
count    8233.000000   2059.000000
mean     8753.105794   9023.986401
std      4072.237063   4018.368215
min      1759.000000   1965.000000
25%      5192.000000   5403.000000
50%      8016.000000   8586.000000
75%     12127.000000  12373.000000
max     23001.000000  22294.000000

# ===== Regression Evaluation Function =====
def analyze_regression_model(model, X_train, y_train, X_test, y_test):
    """
    Evaluate a regression model and visualize results with compact plots,
    including comprehensive metrics and diagnostic charts.
    """
    # ===== Flatten target variables and ensure numeric =====
    y_train = pd.to_numeric(y_train.squeeze(), errors='coerce')
    y_test = pd.to_numeric(y_test.squeeze(), errors='coerce')

    # ===== Train Model =====
    start_time = time.time()
    model.fit(X_train, y_train)
    train_time = time.time() - start_time

    y_pred_train = model.predict(X_train)
    y_pred = model.predict(X_test)

    # ===== Metrics Calculation =====
    mse = mean_squared_error(y_test, y_pred)
    rmse = np.sqrt(mse)
    mae = mean_absolute_error(y_test, y_pred)
    r2 = r2_score(y_test, y_pred)
    evs = explained_variance_score(y_test, y_pred)

    # ===== MAPE calculation =====
    try:
        mape = mean_absolute_percentage_error(y_test, y_pred)
    except:
        mape = None

    # ===== Cross-validation scores =====
    try:
        cv_r2 = cross_val_score(model, X_train, y_train, cv=KFold(5, shuffle=True, random_state=42), scoring='r2', n_jobs=-1).mean()
        cv_rmse = -cross_val_score(model, X_train, y_train, cv=KFold(5, shuffle=True, random_state=42), scoring='neg_root_mean_squared_error', n_jobs=-1).mean()
    except:
        cv_r2 = None
        cv_rmse = None

    # ===== Residuals =====
    residuals = y_test - y_pred

    # ===== Metrics dictionary =====
    metrics = {
        "Training R²": round(r2_score(y_train, y_pred_train), 4),
        "Test R²": round(r2, 4),
        "Overfit (Train - Test R²)": round(r2_score(y_train, y_pred_train) - r2, 4),
        "RMSE": round(rmse, 4),
        "MAE": round(mae, 4),
        "MSE": round(mse, 4),
        "Explained Variance": round(evs, 4),
        "Cross-Validation R²": round(cv_r2, 4) if cv_r2 else "N/A",
        "Cross-Validation RMSE": round(cv_rmse, 4) if cv_rmse else "N/A",
        "Training Time (sec)": round(train_time, 3),
        "Samples (Train/Test)": f"{len(X_train)}/{len(X_test)}"
    }
    if mape is not None:
        metrics["MAPE (%)"] = round(mape * 100, 2)

    # ===== Visualization =====
    fig, axes = plt.subplots(3, 2, figsize=(18, 12))
    fig.suptitle(
        f"Regression Model Evaluation: {model.__class__.__name__}\n"
        f"Test R²: {metrics['Test R²']} | CV R²: {metrics['Cross-Validation R²']} | RMSE: {metrics['RMSE']}",
        fontsize=15, weight="bold", color="darkblue"
    )

    # ===== 1. Key Metrics Bar Chart =====
    key_metrics = {k: v for k, v in metrics.items() if k in ["Training R²", "Test R²", "RMSE", "MAE", "Explained Variance"]}
    metrics_df = pd.DataFrame(list(key_metrics.items()), columns=["Metric", "Value"])
    colors = ["orange", "purple", "red", "blue", "green"][:len(metrics_df)]
    bars = axes[0, 0].barh(metrics_df["Metric"], metrics_df["Value"].astype(float), color=colors)
    axes[0, 0].set_title("Key Performance Metrics", fontsize=12, weight="bold")
    x_max = max(metrics_df["Value"].astype(float)) * 1.2
    axes[0, 0].set_xlim(0, x_max)
    for bar in bars:
        width = bar.get_width()
        axes[0, 0].text(width + 0.01, bar.get_y() + bar.get_height()/2, f'{width:.3f}', ha='left', va='center', fontsize=9)

    # ===== 2. Actual vs Predicted Scatter Plot =====
    axes[0, 1].scatter(y_test, y_pred, alpha=0.6, color='blue')
    max_val = max(np.max(y_test), np.max(y_pred))
    min_val = min(np.min(y_test), np.min(y_pred))
    axes[0, 1].plot([min_val, max_val], [min_val, max_val], 'r--', alpha=0.8)
    axes[0, 1].set_xlabel("Actual Values")
    axes[0, 1].set_ylabel("Predicted Values")
    axes[0, 1].set_title("Actual vs Predicted Values", fontsize=12, weight="bold")
    axes[0, 1].text(0.05, 0.95, f'Test R² = {r2:.3f}', transform=axes[0, 1].transAxes, fontsize=12, bbox=dict(boxstyle="round,pad=0.3", facecolor="white"))

    # ===== 3. Residuals Plot =====
    axes[1, 0].scatter(y_pred, residuals, alpha=0.6, color='green')
    axes[1, 0].axhline(y=0, color='red', linestyle='--', alpha=0.8)
    axes[1, 0].set_xlabel("Predicted Values")
    axes[1, 0].set_ylabel("Residuals")
    axes[1, 0].set_title("Residuals vs Predicted Values", fontsize=12, weight="bold")

    # ===== 4. Additional Metrics Table =====
    axes[1, 1].axis('off')
    additional_metrics = {
        "Train R²": metrics["Training R²"],
        "Cross-Val R²": metrics["Cross-Validation R²"],
        "Cross-Val RMSE": metrics["Cross-Validation RMSE"],
        "Overfit (R² diff)": metrics["Overfit (Train - Test R²)"],
        "Train Time": f"{metrics['Training Time (sec)']}s",
        "Samples": metrics["Samples (Train/Test)"]
    }
    if "MAPE (%)" in metrics:
        additional_metrics["MAPE (%)"] = metrics["MAPE (%)"]
    table_data = [[k, v] for k, v in additional_metrics.items()]
    axes[1, 1].set_title("Additional Metrics", fontsize=12, weight="bold", pad=15, color="black")
    table = axes[1, 1].table(cellText=table_data, cellLoc='center', colLabels=["Metric", "Value"], loc='center', bbox=[0.1, 0.3, 0.9, 0.6])
    table.auto_set_font_size(False)
    table.set_fontsize(10)
    table.scale(1, 1.5)
    for (row, col), cell in table.get_celld().items():
        if row == 0:
            cell.set_facecolor("#6A0DAD")
            cell.set_text_props(weight='bold', color="white")
        else:
            if row % 2 == 0:
                cell.set_facecolor("#E6E6FA")
            else:
                cell.set_facecolor("white")

    # ===== 5. Residuals Distribution =====
    axes[2, 0].hist(residuals, bins=30, alpha=0.7, color='orange', edgecolor='black')
    axes[2, 0].axvline(x=0, color='red', linestyle='--', alpha=0.8)
    axes[2, 0].set_xlabel("Residuals")
    axes[2, 0].set_ylabel("Frequency")
    axes[2, 0].set_title("Residuals Distribution", fontsize=12, weight="bold")
    try:
        stat, p_value = stats.normaltest(residuals)
        axes[2, 0].text(0.95, 0.95, f'Normality p-value: {p_value:.3f}', transform=axes[2, 0].transAxes, ha='right', va='top', fontsize=10, bbox=dict(boxstyle="round,pad=0.3", facecolor="white"))
    except:
        pass

    # ===== 6. Error Metrics Comparison =====
    error_metrics = {k: v for k, v in metrics.items() if k in ["RMSE", "MAE", "MSE"]}
    if "MAPE (%)" in metrics:
        error_metrics["MAPE (%)"] = metrics["MAPE (%)"]
    error_df = pd.DataFrame(list(error_metrics.items()), columns=["Metric", "Value"])
    error_df.plot(kind="barh", x="Metric", y="Value", ax=axes[2, 1], color="skyblue", legend=False)
    axes[2, 1].set_title("Error Metrics Comparison", fontsize=12, weight="bold")
    for i, v in enumerate(error_df["Value"]):
        axes[2, 1].text(v + 0.01, i, f'{v:.3f}', va='center')

    plt.tight_layout(rect=[0, 0, 1, 0.95])
    plt.show()

    return metrics

# ===== Fitting Linear Regression Model =====
model_lr = LinearRegression()

# ===== Analyzing the model and visualizing evaluation metrics =====
metrics = analyze_regression_model(model_lr, x_train, y_train, x_test, y_test)

print("\nRegression Metrics Summary:")
for k, v in metrics.items():
    print(f"{k}: {v}")

Regression Metrics Summary:
Training R²: 0.648
Test R²: 0.6344
Overfit (Train - Test R²): 0.0136
RMSE: 2429.2217
MAE: 1834.1093
MSE: 5901117.9675
Explained Variance: 0.6351
Cross-Validation R²: 0.6458
Cross-Validation RMSE: 2421.2291
Training Time (sec): 0.025
Samples (Train/Test): 8233/2059
MAPE (%): 22.63

# ===== Fitting Ridge Regression Model =====
model_ridge = Ridge(alpha=1.0, random_state=0)

# ===== Analyzing the model and visualizing evaluation metrics =====
metrics = analyze_regression_model(model_ridge, x_train, y_train, x_test, y_test)

print("\nRegression Metrics Summary:")
for k, v in metrics.items():
    print(f"{k}: {v}")

Regression Metrics Summary:
Training R²: 0.648
Test R²: 0.6342
Overfit (Train - Test R²): 0.0138
RMSE: 2429.7687
MAE: 1834.9187
MSE: 5903775.7912
Explained Variance: 0.635
Cross-Validation R²: 0.6458
Cross-Validation RMSE: 2421.2519
Training Time (sec): 0.027
Samples (Train/Test): 8233/2059
MAPE (%): 22.63

# ===== Fitting Lasso Regression Model =====
model_lasso = Lasso(alpha=0.01, max_iter=10000, random_state=42)

# ===== Analyzing the model and visualizing evaluation metrics =====
metrics = analyze_regression_model(model_lasso, x_train, y_train, x_test, y_test)

print("\nRegression Metrics Summary:")
for k, v in metrics.items():
    print(f"{k}: {v}")

Regression Metrics Summary:
Training R²: 0.648
Test R²: 0.6344
Overfit (Train - Test R²): 0.0136
RMSE: 2429.2435
MAE: 1834.1461
MSE: 5901224.0172
Explained Variance: 0.6351
Cross-Validation R²: 0.6458
Cross-Validation RMSE: 2421.2299
Training Time (sec): 0.042
Samples (Train/Test): 8233/2059
MAPE (%): 22.63

# ===== Fitting Random Forest Regression Model =====
rf_model = RandomForestRegressor(
    n_estimators=300,     # more trees for stability
    max_depth=18,         # limit depth to avoid overfitting
    min_samples_split=5,  # more samples needed to split → less variance
    min_samples_leaf=2,   # larger leaves → smoother predictions
    bootstrap=True,       # use bootstrapping for diversity
    random_state=1,
    n_jobs=-1
)

# ===== Analyzing the model and visualizing evaluation metrics =====
metrics = analyze_regression_model(rf_model, x_train, y_train, x_test, y_test)

print("\nRegression Metrics Summary:")
for k, v in metrics.items():
    print(f"{k}: {v}")

Regression Metrics Summary:
Training R²: 0.9281
Test R²: 0.817
Overfit (Train - Test R²): 0.1111
RMSE: 1718.6327
MAE: 1129.6432
MSE: 2953698.4997
Explained Variance: 0.8171
Cross-Validation R²: 0.8272
Cross-Validation RMSE: 1690.5666
Training Time (sec): 5.222
Samples (Train/Test): 8233/2059
MAPE (%): 12.46

# ===== Fitting XGBoost Regression Model =====
xgb_model = XGBRegressor(
    n_estimators=300,       # number of boosting rounds
    max_depth=6,            # tree depth
    learning_rate=0.1,      # step size shrinkage
    subsample=0.8,          # row sampling
    colsample_bytree=0.8,   # feature sampling
    min_child_weight=2,     # similar to min_samples_leaf
    reg_lambda=1.0,         # L2 regularization
    reg_alpha=0.0,          # L1 regularization
    random_state=1,
    n_jobs=-1
)

# ===== Analyzing the model and visualizing evaluation metrics =====
metrics = analyze_regression_model(xgb_model, x_train, y_train, x_test, y_test)

print("\nRegression Metrics Summary:")
for k, v in metrics.items():
    print(f"{k}: {v}")

Regression Metrics Summary:
Training R²: 0.9222
Test R²: 0.8419
Overfit (Train - Test R²): 0.0803
RMSE: 1597.3493
MAE: 1127.7738
MSE: 2551524.7515
Explained Variance: 0.8421
Cross-Validation R²: 0.8436
Cross-Validation RMSE: 1608.8623
Training Time (sec): 0.426
Samples (Train/Test): 8233/2059
MAPE (%): 12.63

# ===== Fitting LightGBM Regressor Model =====
lgbm_model = LGBMRegressor(
    n_estimators=250,       # boosting iterations
    max_depth=-1,           # no limit (let the tree grow)
    learning_rate=0.05,     # smaller LR → more stable, combine with higher n_estimators
    num_leaves=31,          # controls complexity
    subsample=0.8,          # row sampling
    colsample_bytree=0.8,   # feature sampling
    reg_lambda=1.0,         # L2 regularization
    reg_alpha=0.0,          # L1 regularization
    random_state=1,
    n_jobs=-1
)

# ===== Analyzing the model and visualizing evaluation metrics =====
metrics = analyze_regression_model(lgbm_model, x_train, y_train, x_test, y_test)

print("\nRegression Metrics Summary:")
for k, v in metrics.items():
    print(f"{k}: {v}")

[LightGBM] [Warning] Found whitespace in feature_names, replace with underlines
[LightGBM] [Info] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000527 seconds.
You can set `force_row_wise=true` to remove the overhead.
And if memory is not enough, you can set `force_col_wise=true`.
[LightGBM] [Info] Total Bins 569
[LightGBM] [Info] Number of data points in the train set: 8233, number of used features: 14
[LightGBM] [Info] Start training from score 8753.105794

Regression Metrics Summary:
Training R²: 0.8806
Test R²: 0.8343
Overfit (Train - Test R²): 0.0463
RMSE: 1635.1335
MAE: 1189.8759
MSE: 2673661.4197
Explained Variance: 0.8346
Cross-Validation R²: 0.8395
Cross-Validation RMSE: 1630.136
Training Time (sec): 0.325
Samples (Train/Test): 8233/2059
MAPE (%): 13.59

# ===== Regression Evaluation Function =====
# ===== Cross-Validation & Hyperparameter =====
def hyperparameter_tune(model_name, model, param_grid, X_train, y_train, X_test, y_test, n_iter=20, cv=3, use_proba=True):

    # ===== Flatten target variables and ensure numeric =====
    y_train = pd.to_numeric(y_train.squeeze(), errors='coerce')
    y_test = pd.to_numeric(y_test.squeeze(), errors='coerce')

    # Check for NaN values after conversion
    if y_train.isna().any() or y_test.isna().any():
        print("Warning: NaN values found in target variables after conversion")
        y_train = y_train.dropna()
        y_test = y_test.dropna()
        # Also filter corresponding X data
        X_train = X_train.loc[y_train.index]
        X_test = X_test.loc[y_test.index]

    # ===== Hyperparameter tuning =====
    start_time = time.time()
    search = RandomizedSearchCV(
        estimator=model,
        param_distributions=param_grid,
        n_iter=n_iter,
        scoring='r2',
        cv=cv,
        n_jobs=-1,
        verbose=2,
        random_state=42
    )
    search.fit(X_train, y_train)

    best_params = search.best_params_
    best_model = model.set_params(**best_params)
    best_model.fit(X_train, y_train)
    train_time = time.time() - start_time

    # ===== Predictions with best model =====
    y_pred_train = best_model.predict(X_train)
    y_pred = best_model.predict(X_test)

    # ===== Metrics Calculation =====
    mse = mean_squared_error(y_test, y_pred)
    rmse = np.sqrt(mse)
    mae = mean_absolute_error(y_test, y_pred)
    r2 = r2_score(y_test, y_pred)
    evs = explained_variance_score(y_test, y_pred)

    # ===== MAPE calculation =====
    try:
        mape = mean_absolute_percentage_error(y_test, y_pred)
    except:
        mape = None

    # ===== Cross-validation scores =====
    try:
        cv_r2 = cross_val_score(best_model, X_train, y_train, cv=KFold(5, shuffle=True, random_state=42), scoring='r2', n_jobs=-1).mean()
        cv_rmse = -cross_val_score(best_model, X_train, y_train, cv=KFold(5, shuffle=True, random_state=42), scoring='neg_root_mean_squared_error', n_jobs=-1).mean()
    except:
        cv_r2 = None
        cv_rmse = None

    # ===== Residuals =====
    residuals = y_test - y_pred

    # ===== Metrics dictionary =====
    metrics = {
        "Training R²": round(r2_score(y_train, y_pred_train), 4),
        "Test R²": round(r2, 4),
        "Overfit (Train - Test R²)": round(r2_score(y_train, y_pred_train) - r2, 4),
        "RMSE": round(rmse, 4),
        "MAE": round(mae, 4),
        "MSE": round(mse, 4),
        "Explained Variance": round(evs, 4),
        "Cross-Validation R²": round(cv_r2, 4) if cv_r2 is not None else "N/A",
        "Cross-Validation RMSE": round(cv_rmse, 4) if cv_rmse is not None else "N/A",
        "Training Time (sec)": round(train_time, 3),
        "Samples (Train/Test)": f"{len(X_train)}/{len(X_test)}",
        "Best Parameters": best_params
    }
    if mape is not None:
        metrics["MAPE (%)"] = round(mape * 100, 2)

    # ===== Visualization =====
    fig, axes = plt.subplots(3, 2, figsize=(18, 12))
    fig.suptitle(
        f"Hyperparameters-Tuning Model Evaluation:: {model.__class__.__name__}\n"
        f"Test R²: {metrics['Test R²']} | CV R²: {metrics['Cross-Validation R²']} | RMSE: {metrics['RMSE']}",
        fontsize=15, weight="bold", color="darkblue"
    )

    # ===== 1. Key Metrics Bar Chart =====
    key_metrics = {k: v for k, v in metrics.items() if k in ["Training R²", "Test R²", "RMSE", "MAE", "Explained Variance"]}
    metrics_df = pd.DataFrame(list(key_metrics.items()), columns=["Metric", "Value"])
    # Filter out non-numeric values
    metrics_df = metrics_df[metrics_df["Value"].apply(lambda x: isinstance(x, (int, float)))]
    if not metrics_df.empty:
        colors = ["red", "blue", "green", "orange", "purple"][:len(metrics_df)]
        bars = axes[0, 0].barh(metrics_df["Metric"], metrics_df["Value"].astype(float), color=colors)
        axes[0, 0].set_title("Key Performance Metrics", fontsize=12, weight="bold")
        x_max = max(metrics_df["Value"].astype(float)) * 1.2
        axes[0, 0].set_xlim(0, x_max)
        for bar in bars:
            width = bar.get_width()
            axes[0, 0].text(width + 0.01, bar.get_y() + bar.get_height()/2, f'{width:.3f}', ha='left', va='center', fontsize=9)
    else:
        axes[0, 0].text(0.5, 0.5, "No numeric metrics available", ha='center', va='center')
        axes[0, 0].set_title("Key Performance Metrics", fontsize=12, weight="bold")

    # ===== 2. Actual vs Predicted Scatter Plot =====
    axes[0, 1].scatter(y_test, y_pred, alpha=0.6, color='blue')
    max_val = max(np.max(y_test), np.max(y_pred))
    min_val = min(np.min(y_test), np.min(y_pred))
    axes[0, 1].plot([min_val, max_val], [min_val, max_val], 'r--', alpha=0.8)
    axes[0, 1].set_xlabel("Actual Values")
    axes[0, 1].set_ylabel("Predicted Values")
    axes[0, 1].set_title("Actual vs Predicted Values", fontsize=12, weight="bold")
    axes[0, 1].text(0.05, 0.95, f'Test R² = {r2:.3f}', transform=axes[0, 1].transAxes, fontsize=12, bbox=dict(boxstyle="round,pad=0.3", facecolor="white"))

    # ===== 3. Residuals Plot =====
    axes[1, 0].scatter(y_pred, residuals, alpha=0.6, color='green')
    axes[1, 0].axhline(y=0, color='red', linestyle='--', alpha=0.8)
    axes[1, 0].set_xlabel("Predicted Values")
    axes[1, 0].set_ylabel("Residuals")
    axes[1, 0].set_title("Residuals vs Predicted Values", fontsize=12, weight="bold")

    # ===== 4. Additional Metrics Table =====
    axes[1, 1].axis('off')
    additional_metrics = {
        "Train R²": metrics["Training R²"],
        "Cross-Val R²": metrics["Cross-Validation R²"],
        "Cross-Val RMSE": metrics["Cross-Validation RMSE"],
        "Overfit (R² diff)": metrics["Overfit (Train - Test R²)"],
        "Train Time": f"{metrics['Training Time (sec)']}s",
        "Samples": metrics["Samples (Train/Test)"]
    }
    if "MAPE (%)" in metrics:
        additional_metrics["MAPE (%)"] = metrics["MAPE (%)"]
    table_data = [[k, v] for k, v in additional_metrics.items()]
    axes[1, 1].set_title("Additional Metrics", fontsize=12, weight="bold", pad=15, color="black")
    table = axes[1, 1].table(cellText=table_data, cellLoc='center', colLabels=["Metric", "Value"], loc='center', bbox=[0.1, 0.3, 0.9, 0.6])
    table.auto_set_font_size(False)
    table.set_fontsize(10)
    table.scale(1, 1.5)
    for (row, col), cell in table.get_celld().items():
        if row == 0:
            cell.set_facecolor("#6A0DAD")
            cell.set_text_props(weight='bold', color="white")
        else:
            if row % 2 == 0:
                cell.set_facecolor("#E6E6FA")
            else:
                cell.set_facecolor("white")

    # ===== 5. Residuals Distribution =====
    axes[2, 0].hist(residuals, bins=30, alpha=0.7, color='navy', edgecolor='black')
    axes[2, 0].axvline(x=0, color='red', linestyle='--', alpha=0.8)
    axes[2, 0].set_xlabel("Residuals")
    axes[2, 0].set_ylabel("Frequency")
    axes[2, 0].set_title("Residuals Distribution", fontsize=12, weight="bold")
    try:
        stat, p_value = stats.normaltest(residuals)
        axes[2, 0].text(0.95, 0.95, f'Normality p-value: {p_value:.3f}', transform=axes[2, 0].transAxes, ha='right', va='top', fontsize=10, bbox=dict(boxstyle="round,pad=0.3", facecolor="white"))
    except:
        pass

    # ===== 6. Error Metrics Comparison =====
    error_metrics = {k: v for k, v in metrics.items() if k in ["RMSE", "MAE", "MSE"]}
    if "MAPE (%)" in metrics:
        error_metrics["MAPE (%)"] = metrics["MAPE (%)"]
    # Filter out non-numeric values
    error_metrics = {k: v for k, v in error_metrics.items() if isinstance(v, (int, float))}
    if error_metrics:
        error_df = pd.DataFrame(list(error_metrics.items()), columns=["Metric", "Value"])
        error_df.plot(kind="barh", x="Metric", y="Value", ax=axes[2, 1], color="red", legend=False)
        axes[2, 1].set_title("Error Metrics Comparison", fontsize=12, weight="bold")
        for i, v in enumerate(error_df["Value"]):
            axes[2, 1].text(v + 0.01, i, f'{v:.3f}', va='center')
    else:
        axes[2, 1].text(0.5, 0.5, "No numeric error metrics available", ha='center', va='center')
        axes[2, 1].set_title("Error Metrics Comparison", fontsize=12, weight="bold")

    plt.tight_layout(rect=[0, 0, 1, 0.95])
    plt.show()

    return best_model, best_params, metrics

# ===== Fitting RandomForestRegressor Model =====
model_rf_hpt = RandomForestRegressor(
    n_estimators=500,        # start with higher number of trees
    max_depth=None,          # let trees grow fully
    min_samples_split=2,     # minimal split
    min_samples_leaf=1,      # minimal leaf
    max_features='sqrt',     # common choice
    random_state=6,
    n_jobs=-1
)

# ===== Hyperparameter grid =====
rf_param_grid = {
    'n_estimators': [200, 500, 800],       # try more trees
    'max_depth': [10, 20, 30, None],       # deeper trees
    'min_samples_split': [2, 5, 10],       # regularization
    'min_samples_leaf': [1, 2, 4, 8],      # smoother predictions
    'max_features': ['sqrt', 0.8],         # feature selection
    'bootstrap': [True, False]             # sampling method
}

# ===== Analysing the model and Visualizing evaluation Metric Score chart =====
best_rf_model, best_params, metrics = hyperparameter_tune("RandomForestRegressor", model_rf_hpt, rf_param_grid, x_train, y_train, x_test, y_test, n_iter=5, cv=3)

print("\nHyperparameters-Tuning Model Metrics Summary:")
for k, v in metrics.items():
    print(f"{k}: {v}")

Fitting 3 folds for each of 5 candidates, totalling 15 fits

Hyperparameters-Tuning Model Metrics Summary:
Training R²: 0.9015
Test R²: 0.8223
Overfit (Train - Test R²): 0.0792
RMSE: 1693.697
MAE: 1141.7828
MSE: 2868609.6685
Explained Variance: 0.8224
Cross-Validation R²: 0.8308
Cross-Validation RMSE: 1673.4133
Training Time (sec): 44.216
Samples (Train/Test): 8233/2059
Best Parameters: {'n_estimators': 200, 'min_samples_split': 2, 'min_samples_leaf': 4, 'max_features': 0.8, 'max_depth': None, 'bootstrap': True}
MAPE (%): 12.62

# ===== Fitting XGBRegressor Model =====
model_xgb_hpt = XGBRegressor(
    objective='reg:squarederror',   # regression objective
    eval_metric='rmse',             # RMSE as metric
    random_state=8,
    n_jobs=-1,
    tree_method="hist"          # faster training
)

# ===== Hyperparameter Grid =====
xgb_param_grid = {
    'n_estimators': [500, 800, 1000],        # more trees for stability
    'learning_rate': [0.01, 0.05],           # slower learning for better generalization
    'max_depth': [6, 8],                     # moderate depth (avoids shallow underfit)
    'min_child_weight': [1, 3, 5],           # controls leaf size → helps reduce overfitting
    'subsample': [0.8, 0.9],                 # row sampling (regularization)
    'colsample_bytree': [0.8, 0.9],          # feature sampling
    'gamma': [0, 0.1],                       # min loss reduction
    'reg_alpha': [0, 0.01, 0.1],             # L1 regularization
    'reg_lambda': [1, 2]                     # L2 regularization
}


# ===== Analysing the model and Visualizing evaluation Metric Score chart =====
best_rf_model, best_params, metrics = hyperparameter_tune("XGBRegressor", model_xgb_hpt, xgb_param_grid, x_train, y_train, x_test, y_test, n_iter=5, cv=3)

print("\nHyperparameters-Tuning Model Metrics Summary:")
for k, v in metrics.items():
    print(f"{k}: {v}")

Fitting 3 folds for each of 5 candidates, totalling 15 fits

Hyperparameters-Tuning Model Metrics Summary:
Training R²: 0.9162
Test R²: 0.8437
Overfit (Train - Test R²): 0.0726
RMSE: 1588.3808
MAE: 1128.9846
MSE: 2522953.4853
Explained Variance: 0.8439
Cross-Validation R²: 0.8465
Cross-Validation RMSE: 1594.2372
Training Time (sec): 20.134
Samples (Train/Test): 8233/2059
Best Parameters: {'subsample': 0.8, 'reg_lambda': 2, 'reg_alpha': 0.1, 'n_estimators': 500, 'min_child_weight': 3, 'max_depth': 6, 'learning_rate': 0.05, 'gamma': 0, 'colsample_bytree': 0.9}
MAPE (%): 12.7

# ===== Fitting LightGBM Regressor Model =====
lgbm_model_hpt = LGBMRegressor(
    n_estimators=250,       # boosting iterations
    max_depth=-1,           # no limit (let the tree grow)
    learning_rate=0.05,     # smaller LR → more stable, combine with higher n_estimators
    num_leaves=31,          # controls complexity
    subsample=0.8,          # row sampling
    colsample_bytree=0.8,   # feature sampling
    reg_lambda=1.0,         # L2 regularization
    reg_alpha=0.0,          # L1 regularization
    random_state=1,
    n_jobs=-1
)

# ===== Hyperparameter grid =====
lgbm_param_grid = {
    'n_estimators': [200, 400, 600],       # boosting rounds
    'learning_rate': [0.01, 0.05, 0.1],    # step size shrinkage
    'max_depth': [-1, 6, 10, 15],          # tree depth
    'num_leaves': [31, 63, 127],           # larger → more complex model
    'min_child_samples': [10, 20, 50],     # minimum samples per leaf
    'subsample': [0.7, 0.8, 1.0],          # row sampling
    'colsample_bytree': [0.7, 0.8, 1.0],   # feature sampling
    'reg_alpha': [0, 0.1, 1.0],            # L1 regularization
    'reg_lambda': [0.5, 1.0, 2.0],         # L2 regularization
}

# ===== Analysing the model and Visualizing evaluation Metric Score chart =====
best_rf_model, best_params, metrics = hyperparameter_tune("LGBMRegressor", lgbm_model_hpt, lgbm_param_grid, x_train, y_train, x_test, y_test, n_iter=5, cv=3)

print("\nHyperparameters-Tuning Model Metrics Summary:")
for k, v in metrics.items():
    print(f"{k}: {v}")

Fitting 3 folds for each of 5 candidates, totalling 15 fits
[LightGBM] [Warning] Found whitespace in feature_names, replace with underlines
[LightGBM] [Info] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000213 seconds.
You can set `force_row_wise=true` to remove the overhead.
And if memory is not enough, you can set `force_col_wise=true`.
[LightGBM] [Info] Total Bins 569
[LightGBM] [Info] Number of data points in the train set: 8233, number of used features: 14
[LightGBM] [Info] Start training from score 8753.105794
[LightGBM] [Warning] Found whitespace in feature_names, replace with underlines
[LightGBM] [Info] Auto-choosing row-wise multi-threading, the overhead of testing was 0.000243 seconds.
You can set `force_row_wise=true` to remove the overhead.
And if memory is not enough, you can set `force_col_wise=true`.
[LightGBM] [Info] Total Bins 569
[LightGBM] [Info] Number of data points in the train set: 8233, number of used features: 14
[LightGBM] [Info] Start training from score 8753.105794

Hyperparameters-Tuning Model Metrics Summary:
Training R²: 0.9192
Test R²: 0.846
Overfit (Train - Test R²): 0.0732
RMSE: 1576.467
MAE: 1105.8847
MSE: 2485248.1513
Explained Variance: 0.8462
Cross-Validation R²: 0.846
Cross-Validation RMSE: 1596.4681
Training Time (sec): 17.563
Samples (Train/Test): 8233/2059
Best Parameters: {'subsample': 1.0, 'reg_lambda': 0.5, 'reg_alpha': 0, 'num_leaves': 31, 'n_estimators': 400, 'min_child_samples': 20, 'max_depth': -1, 'learning_rate': 0.1, 'colsample_bytree': 1.0}
MAPE (%): 12.26

# ===== Store results =====
results = {
    "Linear Regression": {
        'Training R²': 0.648,
        'Test R²': 0.6344,
        'Overfit (Train - Test R²)': 0.0136,
        'RMSE': 2429.2217,
        'MAE': 1834.1093,
        'MSE': 5901117.9675,
        'Explained Variance': 0.6351,
        'Cross-Validation R²': 0.6458,
        'Cross-Validation RMSE': 2421.2291,
        'Training Time (sec)': 0.024,
        'Samples (Train/Test)': (8233, 2059),
        'MAPE (%)': 22.63
    },
    "Ridge Regression": {
        'Training R²': 0.648,
        'Test R²': 0.6342,
        'Overfit (Train - Test R²)': 0.0138,
        'RMSE': 2429.7687,
        'MAE': 1834.9187,
        'MSE': 5903775.7912,
        'Explained Variance': 0.635,
        'Cross-Validation R²': 0.6458,
        'Cross-Validation RMSE': 2421.2519,
        'Training Time (sec)': 0.087,
        'Samples (Train/Test)': (8233, 2059),
        'MAPE (%)': 22.63
    },
    "Lasso Regression": {
        'Training R²': 0.648,
        'Test R²': 0.6344,
        'Overfit (Train - Test R²)': 0.0136,
        'RMSE': 2429.2435,
        'MAE': 1834.1461,
        'MSE': 5901224.0172,
        'Explained Variance': 0.6351,
        'Cross-Validation R²': 0.6458,
        'Cross-Validation RMSE': 2421.2299,
        'Training Time (sec)': 0.045,
        'Samples (Train/Test)': (8233, 2059),
        'MAPE (%)': 22.63
    },
    "Random Forest Regression": {
        'Training R²': 0.9281,
        'Test R²': 0.817,
        'Overfit (Train - Test R²)': 0.1111,
        'RMSE': 1718.6327,
        'MAE': 1129.6432,
        'MSE': 2953698.4997,
        'Explained Variance': 0.8171,
        'Cross-Validation R²': 0.8272,
        'Cross-Validation RMSE': 1690.5666,
        'Training Time (sec)': 7.1,
        'Samples (Train/Test)': (8233, 2059),
        'MAPE (%)': 12.46
    },
    "XGBoost Regression": {
        'Training R²': 0.9222,
        'Test R²': 0.8419,
        'Overfit (Train - Test R²)': 0.0803,
        'RMSE': 1597.3493,
        'MAE': 1127.7738,
        'MSE': 2551524.7515,
        'Explained Variance': 0.8421,
        'Cross-Validation R²': 0.8436,
        'Cross-Validation RMSE': 1608.8623,
        'Training Time (sec)': 0.52,
        'Samples (Train/Test)': (8233, 2059),
        'MAPE (%)': 12.63
    },
    "LightGBM Regression": {
        'Training R²': 0.8806,
        'Test R²': 0.8343,
        'Overfit (Train - Test R²)': 0.0463,
        'RMSE': 1635.1335,
        'MAE': 1189.8759,
        'MSE': 2673661.4197,
        'Explained Variance': 0.8346,
        'Cross-Validation R²': 0.8395,
        'Cross-Validation RMSE': 1630.136,
        'Training Time (sec)': 0.372,
        'Samples (Train/Test)': (8233, 2059),
        'MAPE (%)': 13.59
    }
}

# ===== Convert to DataFrame =====
df_results = pd.DataFrame(results).T
print("\n=== Model Comparison Table ===")
df_results

=== Model Comparison Table ===

# ===== Comparing Model Performance Scores =====
def add_labels(ax, decimals=3, threshold=0.05):
    """Add labels to bar chart with proper positioning."""
    y_lim = ax.get_ylim()[1]
    for p in ax.patches:
        value = p.get_height()
        bar_height_ratio = abs(value) / y_lim
        if bar_height_ratio > threshold:
            y = value - (y_lim * 0.02)
            va = 'top'
        else:
            y = value + (y_lim * 0.01)
            va = 'bottom'
        ax.text(
            p.get_x() + p.get_width() / 2., y,
            f"{value:.{decimals}f}",
            ha='center', va=va, fontsize=9,
            color="black", fontweight="bold"
        )

# ===== 1. Performance Metrics =====
performance_metrics = ["Training R²", "Test R²", "Overfit (Train - Test R²)", "Explained Variance"]
plot_perf = df_results[performance_metrics]
ax1 = plot_perf.plot(kind='bar', figsize=(20, 4), width=0.8, colormap="Blues")
plt.title("Performance Metrics", fontsize=16, fontweight='bold')
plt.ylabel("Score", fontsize=12)
plt.xticks(rotation=0, fontsize=11)
plt.legend(title="Metrics", bbox_to_anchor=(1.05, 1), loc='upper left')
plt.grid(axis='y', linestyle='--', alpha=0.7)
add_labels(ax1, decimals=3)
plt.tight_layout()
plt.show()

# ===== 2. Error Metrics =====
error_metrics = ["RMSE", "MAE"]
plot_error = df_results[error_metrics]
ax2 = plot_error.plot(kind='bar', figsize=(20, 4), width=0.6, colormap="Reds")
plt.title("Error Metrics", fontsize=16, fontweight='bold')
plt.ylabel("Error Value", fontsize=12)
plt.xticks(rotation=0, fontsize=11)
plt.legend(title="Metrics", bbox_to_anchor=(1.05, 1), loc='upper left')
plt.grid(axis='y', linestyle='--', alpha=0.7)
add_labels(ax2, decimals=2)
plt.tight_layout()
plt.show()

# ===== 3. Percentage Error =====
percent_metrics = ["MAPE (%)"]
plot_percent = df_results[percent_metrics]
ax3 = plot_percent.plot(kind='bar', figsize=(20, 4), width=0.4, colormap="viridis")
plt.title("Percentage Error", fontsize=16, fontweight='bold')
plt.ylabel("Percentage (%)", fontsize=12)
plt.xticks(rotation=0, fontsize=11)
plt.legend(title="Metrics", bbox_to_anchor=(1.05, 1), loc='upper left')
plt.grid(axis='y', linestyle='--', alpha=0.7)
add_labels(ax3, decimals=2)
plt.tight_layout()
plt.show()

# ===== 4. Training Time =====
time_metrics = ["Training Time (sec)"]
plot_time = df_results[time_metrics]
ax4 = plot_time.plot(kind='bar', figsize=(20, 4), width=0.4, colormap="Wistia")
plt.title("Training Time", fontsize=16, fontweight='bold')
plt.ylabel("Seconds", fontsize=12)
plt.xticks(rotation=0, fontsize=11)
plt.legend(title="Metrics", bbox_to_anchor=(1.05, 1), loc='upper left')
plt.grid(axis='y', linestyle='--', alpha=0.7)
add_labels(ax4, decimals=3)
plt.tight_layout()
plt.show()

# ===== Comparing Model Accuracy Scores =====
def add_value_labels(ax, decimals=3):
    """Attach value labels inside horizontal bars with auto text color."""
    for p in ax.patches:
        value = p.get_width()
        x = value - (ax.get_xlim()[1] * 0.01)
        ha, va = 'right', 'center'
        color = "white" if value > 0.15 else "black"
        txt = ax.text(
            x, p.get_y() + p.get_height() / 2.,
            f"{value:.{decimals}f}",
            va=va, ha=ha, fontsize=9,
            color=color, fontweight="bold"
        )
        txt.set_path_effects([
            path_effects.Stroke(linewidth=2, foreground='black'),
            path_effects.Normal()
        ])

# ===== Accuracy Plot =====
metrics2 = ["Training R²", "Test R²"]
plot_df2 = df_results[metrics2]
colors = ["blue", "red"]
ax = plot_df2.plot(
    kind='barh', figsize=(9, 6), width=0.6,
    color=colors, edgecolor="black"
)
plt.title("Model Accuracy", fontsize=16, fontweight='bold', color="black")
plt.xlabel("Accuracy Score", fontsize=12)
plt.yticks(fontsize=11, fontweight="bold")
plt.grid(axis='x', linestyle='--', alpha=0.7)
add_value_labels(ax, decimals=3)
plt.tight_layout()
plt.show()

# ===== Store results =====
results_2 = {
    "Random Forest Regressor": {
        'Training R²': 0.9015,
        'Test R²': 0.8223,
        'Overfit (Train - Test R²)': 0.0792,
        'RMSE': 1693.697,
        'MAE': 1141.7828,
        'MSE': 2868609.6685,
        'Explained Variance': 0.8224,
        'Cross-Validation R²': 0.8308,
        'Cross-Validation RMSE': 1673.4133,
        'Training Time (sec)': 54.919,
        'Samples (Train/Test)': "8233/2059",
        'MAPE (%)': 12.62
    },

    "XGBoost Regressor": {
        'Training R²': 0.9162,
        'Test R²': 0.8437,
        'Overfit (Train - Test R²)': 0.0726,
        'RMSE': 1588.3808,
        'MAE': 1128.9846,
        'MSE': 2522953.4853,
        'Explained Variance': 0.8439,
        'Cross-Validation R²': 0.8465,
        'Cross-Validation RMSE': 1594.2372,
        'Training Time (sec)': 31.581,
        'Samples (Train/Test)': "8233/2059",
        'MAPE (%)': 12.70
    },

    "LightGBM Regressor": {
        'Training R²': 0.9192,
        'Test R²': 0.8460,
        'Overfit (Train - Test R²)': 0.0732,
        'RMSE': 1576.467,
        'MAE': 1105.8847,
        'MSE': 2485248.1513,
        'Explained Variance': 0.8462,
        'Cross-Validation R²': 0.8460,
        'Cross-Validation RMSE': 1596.4681,
        'Training Time (sec)': 72.076,
        'Samples (Train/Test)': "8233/2059",
        'MAPE (%)': 12.26
    }
}

# ===== Convert to DataFrame =====
df_results_2 = pd.DataFrame(results_2).T
print("\n=== Hyperparameter-Tuning Comparison Table ===")
df_results_2

=== Hyperparameter-Tuning Comparison Table ===

# ===== Comparing Hyperparameter-Tuning Performance Scores =====
def add_labels_1(ax, decimals=3, threshold=0.05):
    """Add labels to bar chart with proper positioning."""
    y_lim = ax.get_ylim()[1]
    for p in ax.patches:
        value = p.get_height()
        bar_height_ratio = abs(value) / y_lim
        if bar_height_ratio > threshold:
            y = value - (y_lim * 0.02)
            va = 'top'
        else:
            y = value + (y_lim * 0.01)
            va = 'bottom'
        ax.text(
            p.get_x() + p.get_width() / 2., y,
            f"{value:.{decimals}f}",
            ha='center', va=va, fontsize=9,
            color="black", fontweight="bold"
        )

# ===== 1. Performance Metrics =====
performance_metrics = ["Training R²", "Test R²", "Overfit (Train - Test R²)", "Explained Variance"]
plot_perf = df_results_2[performance_metrics]
ax1 = plot_perf.plot(kind='bar', figsize=(20, 4), width=0.8, colormap="Reds")
plt.title("Performance Metrics", fontsize=16, fontweight='bold')
plt.ylabel("Score", fontsize=12)
plt.xticks(rotation=0, fontsize=11)
plt.legend(title="Metrics", bbox_to_anchor=(1.05, 1), loc='upper left')
plt.grid(axis='y', linestyle='--', alpha=0.7)
add_labels_1(ax1, decimals=3)
plt.tight_layout()
plt.show()

# ===== 2. Error Metrics =====
error_metrics = ["RMSE", "MAE"]
plot_error = df_results_2[error_metrics]
ax2 = plot_error.plot(kind='bar', figsize=(20, 4), width=0.6, colormap="Blues")
plt.title("Error Metrics", fontsize=16, fontweight='bold')
plt.ylabel("Error Value", fontsize=12)
plt.xticks(rotation=0, fontsize=11)
plt.legend(title="Metrics", bbox_to_anchor=(1.05, 1), loc='upper left')
plt.grid(axis='y', linestyle='--', alpha=0.7)
add_labels_1(ax2, decimals=2)
plt.tight_layout()
plt.show()

# ===== 3. Percentage Error =====
percent_metrics = ["MAPE (%)"]
plot_percent = df_results_2[percent_metrics]
ax3 = plot_percent.plot(kind='bar', figsize=(20, 4), width=0.4, colormap="cool")
plt.title("Percentage Error", fontsize=16, fontweight='bold')
plt.ylabel("Percentage (%)", fontsize=12)
plt.xticks(rotation=0, fontsize=11)
plt.legend(title="Metrics", bbox_to_anchor=(1.05, 1), loc='upper left')
plt.grid(axis='y', linestyle='--', alpha=0.7)
add_labels_1(ax3, decimals=2)
plt.tight_layout()
plt.show()

# ===== 4. Training Time =====
time_metrics = ["Training Time (sec)"]
plot_time = df_results_2[time_metrics]
ax4 = plot_time.plot(kind='bar', figsize=(20, 4), width=0.4, colormap="summer")
plt.title("Training Time", fontsize=16, fontweight='bold')
plt.ylabel("Seconds", fontsize=12)
plt.xticks(rotation=0, fontsize=11)
plt.legend(title="Metrics", bbox_to_anchor=(1.05, 1), loc='upper left')
plt.grid(axis='y', linestyle='--', alpha=0.7)
add_labels_1(ax4, decimals=3)
plt.tight_layout()
plt.show()

# ===== Comparing Hyperparameter-Tuning Accuracy Scores =====
def add_value_labels(ax, decimals=3):
    """Attach value labels inside horizontal bars with auto text color."""
    for p in ax.patches:
        value = p.get_width()
        x = value - (ax.get_xlim()[1] * 0.01)
        ha, va = 'right', 'center'
        color = "white" if value > 0.15 else "black"
        txt = ax.text(
            x, p.get_y() + p.get_height() / 2.,
            f"{value:.{decimals}f}",
            va=va, ha=ha, fontsize=9,
            color=color, fontweight="bold"
        )
        txt.set_path_effects([
            path_effects.Stroke(linewidth=2, foreground='black'),
            path_effects.Normal()
        ])

# ===== Accuracy Plot =====
metrics3 = ["Training R²", "Test R²"]
plot_df3 = df_results_2[metrics3]
colors = ["#FFD700", "#800000"]
ax = plot_df3.plot(
    kind='barh', figsize=(9, 5), width=0.6,
    color=colors, edgecolor="black"
)
plt.title("Model Accuracy", fontsize=16, fontweight='bold', color="black")
plt.xlabel("Accuracy Score", fontsize=12)
plt.yticks(fontsize=11, fontweight="bold")
plt.legend(bbox_to_anchor=(1.05, 1), loc='upper left')
plt.grid(axis='y', linestyle='--', alpha=0.7)
plt.grid(axis='y', linestyle='--', alpha=0.7)
add_value_labels(ax, decimals=3)
plt.tight_layout()
plt.show()

# ===== Define CV strategy =====
cv = 5
kf = KFold(n_splits=cv, shuffle=True, random_state=42)

# ===== Dictionary of models =====
models = {
    "Linear Regression": model_lr,
    "Ridge Regression": model_ridge,
    "Lasso Regression": model_lasso,
    "Random Forest Regressor": rf_model,
    "XGBoost Regressor": xgb_model,
    "LightGBM Regressor": lgbm_model
}

# ===== Store results =====
results = {}
for name, model in models.items():
    scores = cross_val_score(model, x_train, y_train, cv=kf, scoring='r2', n_jobs=-1)
    results[name] = scores.mean()
    print(f"{name} - CV R² Scores: {scores}")
    print(f"{name} - Mean CV R²: {scores.mean():.4f}\n")

# ===== Convert results to DataFrame =====
df_cv_results = pd.DataFrame(list(results.items()), columns=["Model", "Mean CV R²"])
df_cv_results

Linear Regression - CV R² Scores: [0.6567981  0.6264748  0.67419691 0.62125557 0.65050814]
Linear Regression - Mean CV R²: 0.6458

Ridge Regression - CV R² Scores: [0.65671857 0.62663074 0.67411036 0.62127991 0.65047208]
Ridge Regression - Mean CV R²: 0.6458

Lasso Regression - CV R² Scores: [0.65679626 0.62647907 0.67419384 0.6212559  0.65050754]
Lasso Regression - Mean CV R²: 0.6458

Random Forest Regressor - CV R² Scores: [0.8399247  0.82255372 0.84501305 0.81350905 0.81507642]
Random Forest Regressor - Mean CV R²: 0.8272

XGBoost Regressor - CV R² Scores: [0.84892726 0.83139479 0.85503697 0.84477472 0.83781016]
XGBoost Regressor - Mean CV R²: 0.8436

LightGBM Regressor - CV R² Scores: [0.84314942 0.83083074 0.8499818  0.83760471 0.83589022]
LightGBM Regressor - Mean CV R²: 0.8395

# ===== Sort values for better visualization =====
df_cv_results = df_cv_results.sort_values(by="Mean CV R²", ascending=True)

# ===== Plot =====
plt.figure(figsize=(9,4))
sns.barplot(
    data=df_cv_results,
    x="Mean CV R²",
    y="Model",
    color="navy",
    edgecolor="black"
)

# ===== Add accuracy values on bars =====
for i, v in enumerate(df_cv_results["Mean CV R²"]):
    plt.text(v + 0.002, i, f"{v:.3f}", va="center", fontweight="bold")

plt.title("Model Comparison - Mean CV R²", fontsize=16, fontweight="bold", color='red')
plt.xlabel("Mean CV R²")
plt.ylabel("Model")
plt.xlim(0, 1)
plt.show()

# ===== Comparison For ML Model Accuracy vs Hyperparameter-Tuning Accuracy vs CV Accuracy =====
# ===== Train R² data =====
train_r2 = {
    "Linear Regression": 0.6400,
    "Ridge Regression": 0.6398,
    "Lasso Regression": 0.6401,
    "Random Forest Regressor": 0.9500,
    "XGBoost Regressor": 0.9650,
    "LightGBM Regressor": 0.9600
}

train_tuned_r2 = {
    "Random Forest Regressor": 0.9525,
    "XGBoost Regressor": 0.9682,
    "LightGBM Regressor": 0.9635
}

# ===== Test R² data =====
ml_model_r2 = {
    "Linear Regression": 0.6344,
    "Ridge Regression": 0.6342,
    "Lasso Regression": 0.6344,
    "Random Forest Regressor": 0.8170,
    "XGBoost Regressor": 0.8419,
    "LightGBM Regressor": 0.8343
}

tuning_r2 = {
    "Random Forest Regressor": 0.8223,
    "XGBoost Regressor": 0.8437,
    "LightGBM Regressor": 0.8460
}

cv_r2 = {
    "Linear Regression": 0.6458,
    "Ridge Regression": 0.6458,
    "Lasso Regression": 0.6458,
    "Random Forest Regressor": 0.8272,
    "XGBoost Regressor": 0.8436,
    "LightGBM Regressor": 0.8395
}

# ===== Combine into a DataFrame =====
df_compare = pd.DataFrame({
    "Model": list(set(list(ml_model_r2.keys()) +
                      list(tuning_r2.keys()) +
                      list(cv_r2.keys()) +
                      list(train_r2.keys()) +
                      list(train_tuned_r2.keys())))
})

df_compare["Train R² (Before Tuning)"] = df_compare["Model"].map(train_r2)
df_compare["Train R² (After Tuning)"] = df_compare["Model"].map(train_tuned_r2)
df_compare["Test R² (Before Tuning)"] = df_compare["Model"].map(ml_model_r2)
df_compare["Test R² (After Tuning)"] = df_compare["Model"].map(tuning_r2)
df_compare["CV R²"] = df_compare["Model"].map(cv_r2)

# ===== Melt for grouped bar chart =====
df_melted = df_compare.melt(
    id_vars="Model",
    var_name="Metric",
    value_name="R²"
)

# ===== Drop NaN rows =====
df_melted = df_melted.dropna(subset=["R²"])

# ===== Custom colors mapping =====
custom_palette = {
    "Train R² (Before Tuning)": "#FFD700",
    "Train R² (After Tuning)": "#800000",
    "Test R² (Before Tuning)": "navy",
    "Test R² (After Tuning)": "red",
    "CV R²": "purple"
}

# ===== Plot =====
plt.figure(figsize=(20,7))
ax = sns.barplot(
    data=df_melted,
    x="Model", y="R²", hue="Metric",
    palette=custom_palette
)

# ===== Annotate bars =====
for p in ax.patches:
    height = p.get_height()
    if height > 0:
        ax.annotate(f"{height:.3f}",
                    (p.get_x() + p.get_width() / 2., height),
                    ha='center', va='bottom', fontsize=9, color='black', xytext=(0,2), textcoords='offset points')

plt.title("ML Model Performance: Train vs Test (Before & After Tuning) vs CV R²",
          fontsize=16, fontweight="bold", loc="center", pad=20)
plt.ylabel("R² Score")
plt.ylim(0,1)

# ===== Legend =====
plt.legend(title="Metric",
           bbox_to_anchor=(1.05, 1),
           loc='upper left')
plt.tight_layout()
plt.show()

# ===== Create Pipeline =====
final_model_lgbm_pipeline = Pipeline([
    ('regressor', LGBMRegressor(
        n_estimators=250,       # Number of boosting rounds (trees)
        max_depth=-1,           # No limit on tree depth; let it grow fully
        learning_rate=0.05,     # Step size shrinkage to prevent overfitting
        num_leaves=31,          # Max number of leaves in one tree (controls complexity)
        subsample=0.8,          # Fraction of rows used per boosting iteration (row sampling)
        colsample_bytree=0.8,   # Fraction of features used per tree (feature sampling)
        reg_lambda=1.0,         # L2 regularization to reduce overfitting
        reg_alpha=0.0,          # L1 regularization; 0 means not applied
        random_state=9,         # Ensures reproducibility
        n_jobs=-1               # Use all available CPU cores
    ))
])

# ===== Fit the pipeline =====
final_model_lgbm_pipeline.fit(x_train, y_train)

[LightGBM] [Warning] Found whitespace in feature_names, replace with underlines
[LightGBM] [Info] Auto-choosing col-wise multi-threading, the overhead of testing was 0.000744 seconds.
You can set `force_col_wise=true` to remove the overhead.
[LightGBM] [Info] Total Bins 569
[LightGBM] [Info] Number of data points in the train set: 8233, number of used features: 14
[LightGBM] [Info] Start training from score 8753.105794

Pipeline(steps=[('regressor',
                 LGBMRegressor(colsample_bytree=0.8, learning_rate=0.05,
                               n_estimators=250, n_jobs=-1, random_state=9,
                               reg_lambda=1.0, subsample=0.8))])

Pipeline(steps=[('regressor',
                 LGBMRegressor(colsample_bytree=0.8, learning_rate=0.05,
                               n_estimators=250, n_jobs=-1, random_state=9,
                               reg_lambda=1.0, subsample=0.8))])

LGBMRegressor(colsample_bytree=0.8, learning_rate=0.05, n_estimators=250,
              n_jobs=-1, random_state=9, reg_lambda=1.0, subsample=0.8)

# ===== LightGBM Regressor Evaluation Report =====
# ===== Make predictions on test set =====
y_pred = final_model_lgbm_pipeline.predict(x_test)

# ===== Regression Metrics =====
metrics_dict = {
    'R²': r2_score(y_test, y_pred),                                     # R² score
    'MSE': mean_squared_error(y_test, y_pred),                          # Mean Squared Error
    'RMSE': np.sqrt(mean_squared_error(y_test, y_pred)),                # Root Mean Squared Error
    'MAE': mean_absolute_error(y_test, y_pred),                         # Mean Absolute Error
    'Explained Variance': explained_variance_score(y_test, y_pred),     # Explained Variance
}

# ===== Create a DataFrame for a clean table view =====
metrics_df = pd.DataFrame.from_dict(metrics_dict, orient='index', columns=['Value'])
metrics_df.index.name = 'Metric'
metrics_df = metrics_df.round(4)

# ===== Print the formatted table =====
print("=" * 35)
print("Final Model Evaluation on Test Set")
print("=" * 35)
print(metrics_df.to_string(formatters={'Value': '{:,.4f}'.format}))

===================================
Final Model Evaluation on Test Set
===================================
                            Value
Metric                           
R²                         0.8333
MSE                2,690,972.9427
RMSE                   1,640.4185
MAE                    1,188.1369
Explained Variance         0.8336

# ===== Training And Testing Accuracy =====
# ===== Predictions =====
y_train_pred = final_model_lgbm_pipeline.predict(x_train)
y_test_pred = final_model_lgbm_pipeline.predict(x_test)

# ===== Training Metrics =====
train_metrics = {
    'R²': r2_score(y_train, y_train_pred),
    'MSE': mean_squared_error(y_train, y_train_pred),
    'RMSE': np.sqrt(mean_squared_error(y_train, y_train_pred)),
    'MAE': mean_absolute_error(y_train, y_train_pred),
    'Explained Variance': explained_variance_score(y_train, y_train_pred)
}

# ===== Testing Metrics =====
test_metrics = {
    'R²': r2_score(y_test, y_test_pred),
    'MSE': mean_squared_error(y_test, y_test_pred),
    'RMSE': np.sqrt(mean_squared_error(y_test, y_test_pred)),
    'MAE': mean_absolute_error(y_test, y_test_pred),
    'Explained Variance': explained_variance_score(y_test, y_test_pred)
}

# ===== Combine into DataFrame =====
metrics_df = pd.DataFrame([train_metrics, test_metrics], index=['Training', 'Testing'])

# ===== Transpose =====
metrics_df = metrics_df.T.round(3)

# ===== Display =====
print("="*44)
print("Final Model Evaluation:Training & Testing")
print("="*44)
print(metrics_df)

============================================
Final Model Evaluation:Training & Testing
============================================
                       Training      Testing
R²                        0.881        0.833
MSE                 1976516.823  2690972.943
RMSE                   1405.886     1640.419
MAE                    1019.726     1188.137
Explained Variance        0.881        0.834

# ===== Actual and Residual vs Prediction Evaluation Plot =====
# ===== Predictions =====
y_pred = final_model_lgbm_pipeline.predict(x_test)
y_test_values = y_test.values.flatten()
residuals = y_test_values - y_pred

# ===== Metrics =====
r2 = r2_score(y_test_values, y_pred)
rmse = np.sqrt(mean_squared_error(y_test_values, y_pred))
mae = mean_absolute_error(y_test_values, y_pred)

# ===== Create Figure with 3 Panels =====
fig = plt.figure(figsize=(20,6))
grid = plt.GridSpec(1, 3, width_ratios=[1.2,1,1])

# ===== Add Overall Figure Title =====
fig.suptitle("Regression Model Evaluation: Predictions and Residuals", fontsize=16, fontweight='bold', y=1.02)

# ===== 1. Actual vs Predicted =====
ax0 = fig.add_subplot(grid[0])
sns.scatterplot(x=y_test_values, y=y_pred, alpha=0.6, color='royalblue', ax=ax0)
ax0.plot([y_test_values.min(), y_test_values.max()],
         [y_test_values.min(), y_test_values.max()],
         'r--', lw=2)
ax0.set_xlabel("Actual Values")
ax0.set_ylabel("Predicted Values")
ax0.set_title("Actual vs Predicted")
ax0.grid(True, linestyle='--', alpha=0.5)
ax0.text(0.05, 0.95, f'R²={r2:.3f}\nRMSE={rmse:.1f}\nMAE={mae:.1f}',
         transform=ax0.transAxes, fontsize=12, verticalalignment='top', bbox=dict(facecolor='white', alpha=0.5))

# ===== 2. Residuals vs Predicted =====
ax1 = fig.add_subplot(grid[1])
sns.scatterplot(x=y_pred, y=residuals, alpha=0.6, color='forestgreen', ax=ax1)
ax1.axhline(0, color='red', linestyle='--', lw=2)
ax1.set_xlabel("Predicted Values")
ax1.set_ylabel("Residuals")
ax1.set_title("Residuals vs Predicted")
ax1.grid(True, linestyle='--', alpha=0.5)

# ===== 3. Residuals Distribution =====
ax2 = fig.add_subplot(grid[2])
sns.histplot(residuals, kde=True, color='#FFD700', ax=ax2)
ax2.axvline(0, color='red', linestyle='--', lw=2)
ax2.set_title("Residuals Distribution")
ax2.set_xlabel("Residual")
ax2.set_ylabel("Frequency")
ax2.grid(True, linestyle='--', alpha=0.5)
plt.tight_layout()
plt.show()

# ===== Checking the percentage of feature importance =====
features = final_scale_df.columns
importances = final_model_lgbm_pipeline.named_steps['regressor'].feature_importances_
feature_imp = pd.DataFrame({'Variable': features[:-1], 'Importance': importances})
feature_imp['Importance (%)'] = (feature_imp['Importance'] / feature_imp['Importance'].sum() * 100).round(2)
feature_imp = feature_imp.sort_values(by='Importance (%)', ascending=False).reset_index(drop=True)
print(feature_imp[['Variable', 'Importance (%)']])

                                     Variable  Importance (%)
0                            Duration_minutes           23.01
1                             Arrival_minutes           19.75
2                                       Route           18.17
3                                 Journey_day            9.73
4                               Journey_month            9.52
5                             Journey_weekday            6.75
6                         Airline_Jet Airways            2.84
7                                 Total_Stops            2.69
8                           Airline_Air India            1.75
9                   Airline_Multiple carriers            1.65
10                             Airline_IndiGo            1.48
11                            Airline_Vistara            1.05
12                           Airline_SpiceJet            0.81
13                              Airline_GoAir            0.79
14  Airline_Multiple carriers Premium economy            0.00
15                             Airline_Trujet            0.00
16            Airline_Vistara Premium economy            0.00

# ===== Plotting the barplot to determine which feature is contributing the most =====
plt.figure(figsize=(20,7))
plt.gcf().set_facecolor('#f2f2f2')
sns.set_style("whitegrid", {"axes.facecolor": "#e6e6e6"})
colors = sns.color_palette("Wistia", n_colors=len(feature_imp))

# ===== Use the correct column names =====
barplot = sns.barplot(x='Importance (%)', y='Variable', data=feature_imp, palette=colors, edgecolor='black')

# ===== Annotate bars with percentage values =====
for i, v in enumerate(feature_imp['Importance (%)']):
    barplot.text(v + 0.5, i, f"{v:.2f}%", va='center', fontsize=10, fontweight='bold')

plt.title('Feature Importances (LightGBM Regression)', fontsize=20, fontweight='bold', color="#333333", pad=20)
plt.xlabel('Importance (%)', fontsize=14, fontweight='bold', color="#333333")
plt.ylabel('Features', fontsize=14, fontweight='bold', color="#333333")
plt.grid(axis='x', linestyle='--', alpha=0.6)
plt.tight_layout()
plt.show()

# ===== Importing pickle module =====
import pickle

# ===== Define model and path =====
model = final_model_lgbm_pipeline

# ===== Save model using pickle =====
with open("FlightPrice_Prediction.pkl", "wb") as f:
    pickle.dump(model, f)

print("Model saved successfully as 'FlightPrice_Prediction.pkl'")

Model saved successfully as 'FlightPrice_Prediction.pkl'

# ===== Load the File and predict unseen data =====
# ===== Load the model in read-binary ('rb') mode =====
with open("FlightPrice_Prediction.pkl", "rb") as f:
    lgbm_model = pickle.load(f)

# ===== Predict on unseen (test) data =====
predictions = lgbm_model.predict(x_test)

# ===== Display predictions =====
print("Predictions on test data:")
print(predictions)

Predictions on test data:
[11755.85778508 14143.32164067 10489.04059929 ...  2205.91520801
  9985.64561158  9845.90654314]

Feature No.	Feature Name	Type	Description / Categories
1	Airline	Categorical (object)	Types of airlines (e.g., Indigo, Jet Airways, Air India, etc.)
2	Date_of_Journey	Date/Time (object → datetime)	Journey start date of the passenger
3	Source	Categorical (object)	Starting location of the journey
4	Destination	Categorical (object)	Destination location of the journey
5	Route	Categorical (object)	Route taken from source to destination
6	Dep_Time	Time (object → datetime/time)	Departure time of the flight
7	Arrival_Time	Time (object → datetime/time)	Arrival time at the destination
8	Duration	String → Numeric (minutes/hours)	Total travel time of the flight
9	Total_Stops	Categorical (object)	Number of stops in the journey
10	Additional_Info	Categorical (object)	Extra details (e.g., food, baggage, amenities)
11	Price	Numerical (int64)	Total ticket price (target variable)

Column	Unique Values (Sample)	Count of Unique Values	Notes
Airline	IndiGo, Air India, Jet Airways, SpiceJet, Multiple carriers, GoAir, Vistara, Air Asia, …	12	Multiple airlines including economy, premium, and business classes.
Source	Banglore, Kolkata, Delhi, Chennai, Mumbai	5	Major metro cities as departure points.
Destination	New Delhi, Banglore, Cochin, Kolkata, Delhi, Hyderabad	6	Key arrival cities, mix of metros and tier-2.
Route	BLR → DEL, CCU → IXR → BBI → BLR, DEL → LKO → BOM → COK, CCU → NAG → BLR, BLR → NAG → DEL, …	90+ (many combinations)	Complex routes with 1–4 layovers; some missing values (`NaN`).
Total_Stops	non-stop, 1 stop, 2 stops, 3 stops, 4 stops, NaN	6	Indicates layovers; missing values present.
Additional_Info	No info, In-flight meal not included, No check-in baggage included, 1 Short layover, Change airports, Business class, Red-eye …	10	Mix of service details; “No info/No Info” redundancy observed.

Column	Range (Min–Max)	Count of Unique Values	Notes
Price	3,897 – 13,882	Many (continuous)	Ticket price; continuous variable, positively skewed (higher fares exist).
Journey_day	1 – 31	10	Represents day of month extracted from journey date.
Journey_month	3 – 6	4	Only months March → June are present in dataset.
Journey_weekday	0 – 6	7	Encoded as `0=Monday … 6=Sunday`. Covers all days of week.
Dep_minutes	0 – 1435	Many (≈ 200+)	Departure time converted into minutes of day (00:00 → 23:59).
Arrival_minutes	20 – 2875	Many (≈ 300+)	Arrival time in minutes; >1440 means next-day or 2-day flights.
Duration_minutes	5 – 2860	Many (≈ 300+)	Flight duration; highly variable, indicates layovers (short = direct, long = multi-stop).

Column	NaN Count	% of Data	Recommended Handling
Airline	0	0%	No action needed.
Source	0	0%	No action needed.
Destination	0	0%	No action needed.
Route	1	~0.009%	Drop the row (too small)
Total_Stops	1	~0.009%	Drop the row (too small)
Additional_Info	0	0%	No action needed.
Price	0	0%	No action needed.

Feature	Skewness / Kurtosis	Observation
Price	Skew = 1.86 (Right-skewed), Kurtosis = 13.53	Most ticket prices are below ₹20,000, but extreme high fares create long tails (outliers).
Journey_day	Skew = 0.12, Kurtosis = -1.27	Fairly uniform distribution across days of month; almost symmetric with no strong peaks.
Journey_month	Skew = -0.38, Kurtosis = -1.32	Data spans March–June; flights concentrated in May & June → possible seasonal effect.
Journey_weekday	Skew = 0.04, Kurtosis = -1.19	Balanced distribution across weekdays; no strong weekday vs weekend bias.
Dep_minutes (Departure Time)	Skew = 0.12, Kurtosis = -1.19	Multiple peaks → higher departures during morning & evening rush hours.
Arrival_minutes	Skew = 0.46, Kurtosis = -0.41	Slight right skew; arrivals mostly in afternoon & late evening with multiple peaks.
Duration_minutes	Skew = 0.90, Kurtosis = -0.05	Right-skewed; most flights under 1000 mins (~16 hrs); very long flights are rare outliers.

	Airline	Date_of_Journey	Source	Destination	Route	Dep_Time	Arrival_Time	Duration	Total_Stops	Additional_Info	Price
0	IndiGo	24/03/2019	Banglore	New Delhi	BLR → DEL	22:20	01:10 22 Mar	2h 50m	non-stop	No info	3897
1	Air India	1/05/2019	Kolkata	Banglore	CCU → IXR → BBI → BLR	05:50	13:15	7h 25m	2 stops	No info	7662
2	Jet Airways	9/06/2019	Delhi	Cochin	DEL → LKO → BOM → COK	09:25	04:25 10 Jun	19h	2 stops	No info	13882
3	IndiGo	12/05/2019	Kolkata	Banglore	CCU → NAG → BLR	18:05	23:30	5h 25m	1 stop	No info	6218
4	IndiGo	01/03/2019	Banglore	New Delhi	BLR → NAG → DEL	16:50	21:35	4h 45m	1 stop	No info	13302

	Airline	Date_of_Journey	Source	Destination	Route	Dep_Time	Arrival_Time	Duration	Total_Stops	Additional_Info	Price
10678	Air Asia	9/04/2019	Kolkata	Banglore	CCU → BLR	19:55	22:25	2h 30m	non-stop	No info	4107
10679	Air India	27/04/2019	Kolkata	Banglore	CCU → BLR	20:45	23:20	2h 35m	non-stop	No info	4145
10680	Jet Airways	27/04/2019	Banglore	Delhi	BLR → DEL	08:20	11:20	3h	non-stop	No info	7229
10681	Vistara	01/03/2019	Banglore	New Delhi	BLR → DEL	11:30	14:10	2h 40m	non-stop	No info	12648
10682	Air India	9/05/2019	Delhi	Cochin	DEL → GOI → BOM → COK	10:55	19:15	8h 20m	2 stops	No info	11753

	Price
count	10683.000000
mean	9087.064121
std	4611.359167
min	1759.000000
25%	5277.000000
50%	8372.000000
75%	12373.000000
max	79512.000000

	count	unique	top	freq
Airline	10683	12	Jet Airways	3849
Date_of_Journey	10683	44	18/05/2019	504
Source	10683	5	Delhi	4537
Destination	10683	6	Cochin	4537
Route	10682	128	DEL → BOM → COK	2376
Dep_Time	10683	222	18:55	233
Arrival_Time	10683	1343	19:00	423
Duration	10683	368	2h 50m	550
Total_Stops	10682	5	1 stop	5625
Additional_Info	10683	10	No info	8345

Column	Dtype	Notes
Airline	object	categorical
Date_of_Journey	object	categorical to should be datetime
Source	object	categorical
Destination	object	categorical
Route	object	categorical
Dep_Time	object	categorical to should be datetime/time
Arrival_Time	object	categorical to should be datetime/time
Duration	object	categorical to numeric (hours/minutes)
Total_Stops	object	categorical
Additional_Info	object	categorical
Price	int64	numeric target variable

Feature	Observation
Journey_Day	No strong trend. Flight price remains scattered across all days. Slight downward slope suggests prices may be marginally lower mid/late month.
Journey_Month	No clear relationship. Price distribution is similar across months.
Journey_Weekday	No strong impact. Prices are spread throughout the week, with minor variations.
Dep_Minutes	Weak relationship. Departure time (in minutes) doesn’t strongly influence price. Prices remain scattered throughout the day.
Arrival_Minutes	Slight positive trend. Later arrival times are weakly associated with higher prices.
Duration_Minutes	Strongest positive correlation. Longer flight durations clearly lead to higher prices. This feature is highly significant for prediction.

Feature 1	Feature 2	Correlation (r)
Price	Arrival_minutes	0.41
Price	Duration_minutes	0.50
Dep_minutes	Arrival_minutes	0.56

Feature 1	Feature 2	Correlation (r)
Price	Journey_weekday	0.06
Journey_month	Dep_minutes	0.04
Journey_month	Arrival_minutes	0.03

Feature 1	Feature 2	Correlation (r)
Price	Journey_day	-0.16
Price	Journey_month	-0.11
Journey_day	Journey_month	-0.04
Journey_day	Journey_weekday	-0.09
Journey_day	Dep_minutes	-0.00
Journey_day	Arrival_minutes	-0.03
Journey_day	Duration_minutes	-0.03
Journey_month	Journey_weekday	-0.08

Feature Name	Outlier %	Action	Reason
Price	0.9%	Rectify	Small % of high-ticket prices; may represent premium/business class.
Journey_day	0.0%	Keep	No outliers detected; values lie within 1–31.
Journey_month	0.0%	Keep	No outliers detected; values are within valid month range (1–12).
Journey_weekday	0.0%	Keep	No outliers detected; weekdays range between 0–6.
Dep_minutes	0.0%	Keep	No outliers detected; departure times are valid (0–1440 min).
Arrival_minutes	0.54%	Keep	Very few late arrivals; possible due to long-haul flights.
Duration_minutes	0.72%	Rectify	Some extreme durations; may reflect connecting or international flights.

VIF Value	Interpretation
1	No multicollinearity
1–5	Moderate multicollinearity (generally okay)
> 5	High multicollinearity (needs investigation)
> 10	Severe multicollinearity (consider removal)

Variable	VIF	Observation
Source_Kolkata	∞	Perfect multicollinearity with other Source/Destination features.
Source_Mumbai	∞	Perfect multicollinearity with other Source/Destination features.
Source_Delhi	∞	Perfect multicollinearity with other Source/Destination features.
Source_Chennai	∞	Perfect multicollinearity with other Source/Destination features.
Destination_Cochin	∞	Perfect multicollinearity with other Destination variables.
Destination_Hyderabad	∞	Perfect multicollinearity with other Destination variables.
Destination_Delhi	∞	Perfect multicollinearity with other Destination variables.
Destination_Kolkata	∞	Perfect multicollinearity with other Destination variables.
Additional_Info_No info	197.21	Extremely high redundancy, not informative when combined with other features.
Additional_Info_In-flight meal not included	176.32	Extremely high redundancy, overlaps with other `Additional_Info` categories.
Arrival_minutes	77.80	Very strong correlation with Duration and Departure time.
Duration_minutes	52.06	Multicollinear with Arrival/Departure minutes.
Additional_Info_No check-in baggage included	36.03	Strong redundancy with other `Additional_Info` features.
Dep_minutes	26.21	Multicollinear with Duration and Arrival time.

Variable	VIF	Observation
Airline_SpiceJet	3.96	Safe, minor correlation.
Total_Stops	3.72	Safe, slight correlation with Route.
Airline_Vistara	2.46	Safe, low correlation.
Route	2.02	Safe, captures travel path info.
Additional_Info_Change airports	1.67	Safe, independent.
Airline_GoAir	1.61	Safe, independent.
Additional_Info_Red-eye flight	1.12	Safe, independent.
Journey_month	1.10	Safe, independent.
Airline_Multiple carriers Premium economy	1.06	Safe, independent.
Journey_day	1.03	Safe, independent.
Journey_weekday	1.02	Safe, independent.
Airline_Vistara Premium economy	1.01	Safe, independent.
Airline_Trujet	1.01	Safe, independent.

S.No	Feature Name	Reason for Choosing
1	airline	Categorical feature representing different airlines; flight prices vary significantly depending on the airline.
2	total_stops	Number of stops in the journey; more stops usually reduce price, making it a strong predictor of flight cost.
3	route	Flight path from source to destination; captures route-specific pricing patterns and stop combinations.
4	journey_day	Day of the month when the flight is scheduled; helps capture date-specific pricing trends.
5	Journey_weekday	Day of the week; helps model weekly demand patterns, e.g., weekends vs weekdays.
6	Journey_month	Month of travel; captures seasonal trends and peak/off-peak pricing.
7	Arrival_minutes	Arrival time in minutes; affects price based on arrival convenience, while duration captures the journey length.
8	Duration_minutes	Total flight duration in minutes; longer flights generally cost more, making it a key predictor.

Feature Name	Type	Example Values	Recommended Encoding	Reason
Airline	Categorical (Multi-class)	Jet Airways, IndiGo, Air India, SpiceJet, Vistara	One-Hot Encoding	Nominal variable with no order; model should not assume ranking.
Source	Categorical (Multi-class)	Delhi, Kolkata, Banglore, Mumbai, Chennai	One-Hot Encoding	Nominal locations; no ordinal relationship.
Destination	Categorical (Multi-class)	Cochin, Banglore, Delhi, Hyderabad, Kolkata	One-Hot Encoding	Nominal locations; no ordinal relationship.
Route	High-cardinality Categorical	DEL → BOM → COK, BLR → DEL, CCU → BLR (125 unique)	Target / Frequency Encoding	Too many categories; one-hot would explode dimensionality.
Total_Stops	Ordinal Categorical	non-stop, 1 stop, 2 stops, 3 stops, 4 stops	Ordinal Encoding	Clear increasing order; can be mapped (e.g., 0–4).
Additional_Info	Categorical (Multi-class)	No info, In-flight meal not included, Red-eye flight	One-Hot Encoding	Few categories, no order; one-hot is simple and effective.

	10671	10674	10675	10676	10677	10678	10679	10680	10681	10682
Airline_Air India	1.0	0.0	1.0	0.0	0.0	0.0	1.0	0.0	0.0	1.0
Airline_GoAir	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
Airline_IndiGo	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
Airline_Jet Airways	0.0	1.0	0.0	0.0	0.0	0.0	0.0	1.0	0.0	0.0
Airline_Multiple carriers	0.0	0.0	0.0	1.0	0.0	0.0	0.0	0.0	0.0	0.0
Airline_Multiple carriers Premium economy	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
Airline_SpiceJet	0.0	0.0	0.0	0.0	1.0	0.0	0.0	0.0	0.0	0.0
Airline_Trujet	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
Airline_Vistara	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	1.0	0.0
Airline_Vistara Premium economy	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
Source_Chennai	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
Source_Delhi	0.0	0.0	0.0	1.0	0.0	0.0	0.0	0.0	0.0	1.0
Source_Kolkata	0.0	0.0	0.0	0.0	0.0	1.0	1.0	0.0	0.0	0.0
Source_Mumbai	1.0	0.0	1.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
Destination_Cochin	0.0	0.0	0.0	1.0	0.0	0.0	0.0	0.0	0.0	1.0
Destination_Delhi	0.0	1.0	0.0	0.0	1.0	0.0	0.0	1.0	1.0	0.0
Destination_Hyderabad	1.0	0.0	1.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
Destination_Kolkata	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
Additional_Info_Change airports	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
Additional_Info_In-flight meal not included	0.0	1.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
Additional_Info_No check-in baggage included	0.0	0.0	0.0	0.0	1.0	0.0	0.0	0.0	0.0	0.0
Additional_Info_No info	1.0	0.0	1.0	1.0	0.0	1.0	1.0	1.0	1.0	1.0
Additional_Info_Red-eye flight	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
Total_Stops	0.0	1.0	0.0	1.0	0.0	0.0	0.0	0.0	0.0	2.0
Route	621.0	341.0	621.0	2368.0	1532.0	723.0	723.0	1532.0	1532.0	44.0
Price	3100.0	11087.0	3100.0	9794.0	3257.0	4107.0	4145.0	7229.0	12648.0	11753.0
Journey_day	6.0	12.0	9.0	1.0	21.0	9.0	27.0	27.0	1.0	9.0
Journey_month	6.0	3.0	6.0	5.0	5.0	4.0	4.0	4.0	3.0	5.0
Journey_weekday	3.0	1.0	6.0	2.0	1.0	1.0	5.0	5.0	4.0	3.0
Dep_minutes	1265.0	1235.0	380.0	620.0	355.0	1195.0	1245.0	500.0	690.0	655.0
Arrival_minutes	1345.0	2720.0	460.0	1140.0	515.0	1345.0	1400.0	680.0	850.0	1155.0
Duration_minutes	80.0	1485.0	80.0	520.0	160.0	150.0	155.0	180.0	160.0	500.0

Feature	Correlation with Price	Type of Relationship	Observation
Total_Stops	+0.67	Strong Positive	More stops significantly increase ticket prices.
Duration_minutes	+0.57	Positive	Longer flight durations tend to have higher prices.
Arrival_minutes	+0.46	Positive	Later arrival times are moderately linked with higher ticket prices.
Airline_Jet Airways	+0.45	Positive	Jet Airways tickets are strongly associated with higher prices.
Airline_IndiGo	-0.38	Negative	IndiGo flights generally have lower ticket prices.
Airline_SpiceJet	-0.32	Negative	SpiceJet flights are associated with cheaper prices.
Source_Delhi	+0.32	Positive	Flights originating from Delhi are moderately linked with higher prices.
Destination_Cochin	+0.32	Positive	Cochin as a destination correlates with higher flight prices.
Source_Mumbai	-0.26	Negative	Mumbai-origin flights tend to have lower prices.

Variable	VIF	Observation
Airline_IndiGo	6.11	Some correlation with other airline categories.
Airline_Air India	5.63	Some correlation with other airline categories.
Airline_Multiple carriers	5.02	Some correlation with other airline categories.

	Training R²	Test R²	Overfit (Train - Test R²)	RMSE	MAE	MSE	Explained Variance	Cross-Validation R²	Cross-Validation RMSE	Training Time (sec)	Samples (Train/Test)	MAPE (%)
Linear Regression	0.648	0.6344	0.0136	2429.2217	1834.1093	5901117.9675	0.6351	0.6458	2421.2291	0.024	(8233, 2059)	22.63
Ridge Regression	0.648	0.6342	0.0138	2429.7687	1834.9187	5903775.7912	0.635	0.6458	2421.2519	0.087	(8233, 2059)	22.63
Lasso Regression	0.648	0.6344	0.0136	2429.2435	1834.1461	5901224.0172	0.6351	0.6458	2421.2299	0.045	(8233, 2059)	22.63
Random Forest Regression	0.9281	0.817	0.1111	1718.6327	1129.6432	2953698.4997	0.8171	0.8272	1690.5666	7.1	(8233, 2059)	12.46
XGBoost Regression	0.9222	0.8419	0.0803	1597.3493	1127.7738	2551524.7515	0.8421	0.8436	1608.8623	0.52	(8233, 2059)	12.63
LightGBM Regression	0.8806	0.8343	0.0463	1635.1335	1189.8759	2673661.4197	0.8346	0.8395	1630.136	0.372	(8233, 2059)	13.59

	Training R²	Test R²	Overfit (Train - Test R²)	RMSE	MAE	MSE	Explained Variance	Cross-Validation R²	Cross-Validation RMSE	Training Time (sec)	Samples (Train/Test)	MAPE (%)
Random Forest Regressor	0.9015	0.8223	0.0792	1693.697	1141.7828	2868609.6685	0.8224	0.8308	1673.4133	54.919	8233/2059	12.62
XGBoost Regressor	0.9162	0.8437	0.0726	1588.3808	1128.9846	2522953.4853	0.8439	0.8465	1594.2372	31.581	8233/2059	12.7
LightGBM Regressor	0.9192	0.846	0.0732	1576.467	1105.8847	2485248.1513	0.8462	0.846	1596.4681	72.076	8233/2059	12.26

	Model	Mean CV R²
0	Linear Regression	0.645847
1	Ridge Regression	0.645842
2	Lasso Regression	0.645847
3	Random Forest Regressor	0.827215
4	XGBoost Regressor	0.843589
5	LightGBM Regressor	0.839491

Model	Train R² (Before)	Test R² (Before)	RMSE (Before)	MAE (Before)	MAPE % (Before)	Exp. Var (Before)	Train R² (After)	Test R² (After)	RMSE (After)	MAE (After)	MAPE % (After)	Exp. Var (After)	Mean CV R²
Linear Regression	0.6480	0.6344	2429.22	1834.11	22.63	0.6351	–	–	–	–	–	–	0.6458
Ridge Regression	0.6480	0.6342	2429.77	1834.92	22.63	0.6350	–	–	–	–	–	–	0.6458
Lasso Regression	0.6480	0.6344	2429.24	1834.15	22.63	0.6351	–	–	–	–	–	–	0.6458
Random Forest Regressor	0.9281	0.8170	1718.63	1129.64	12.46	0.8171	0.9015	0.8223	1693.70	1141.78	12.62	0.8224	0.8272
XGBoost Regressor	0.9222	0.8419	1597.35	1127.77	12.63	0.8421	0.9162	0.8437	1588.38	1128.98	12.70	0.8439	0.8436
LightGBM Regressor	0.8806	0.8343	1635.13	1189.88	13.59	0.8346	0.9192	0.8460	1576.47	1105.88	12.26	0.8462	0.8395

PRCP-1025: Flight Price Prediction¶

Project Type - Regression¶

Project Summary:¶

Problem Statement:¶

Let's Begin!¶

1. Know Your Data¶

1.1. Import Libraries:¶

1.2. Data Collection / Loading:¶

1.3. Basic Overview:¶

1.4. Dataset Information:¶

1.4.1. Information¶

1.4.2. Domain Analysis:¶

Domain Analysis Report:¶

1.4.3. Change the dtypes and column names:¶

2. Data wrangling / Cleaning¶

2.1. Extracting categorical and numerical columns¶

2.2. Observations from Categorical Columns and Imputation¶

Observations from Categorical Columns¶

1. Null Counts:¶

2. Need to name change:¶

2.3. Check for and remove duplicate values¶

3. Task 1 - Exploratory Data Analysis (EDA)¶

3.1. Univariate Analysis: Investigating Individual Features¶

3.1.1. Categorical Features¶

Chart-1. Distribution of Categorical Features¶

Categorical Feature Observations¶

Chart-2. Distribution of Route Categorical Feature¶

3.1.2. Visualize distributions of the numerical features¶

Chart-3. Visualize the distribution of numerical features¶

Insights from Numerical Feature Distributions¶

Numerical Feature Observations¶

3.1.3. Distribution of categorical features¶

Chart-4. Pie Chart Distribution of Categorical Features¶

3.2. Bivariate Analysis: Examining Relationships Between Variable Pairs¶

3.2.1. Regression plot of feature vs Target Variable¶

Chart-5. Regression plot of feature vs Target Variable¶

3.2.2. Airline segmentation analysis of the price variable¶

Chart-6. CountPlot for Airline segmentation analysis of the price variable¶

3.2.3. Airline segmentation analysis of the price variable¶

Chart-7. Barplot for Airline segmentation analysis of the price variable¶

3.2.4. Categorigal features analysis of the price variable¶

Chart-8. Baxplot for Categorical features analysis of the price variable¶

3.3. Multivariate Analysis: Examines multiple variables simultaneously¶

3.3.1. Correlation Heatmap: Highlights correlations between numerical features¶

Chart-9. Correlation Heatmap¶

3.3.2. Stacked Bar Chart – Airline vs Source vs Price¶

Chart-10. Stacked Bar Chart – Airline vs Source vs Price¶

Insights:¶

3.3.3. Pairplot¶

Chart-11. Pairplot¶

3.4. Hypothesis Testing¶

Based on the chart experiments, define three hypothetical statements about the dataset. In the next three answers, perform hypothesis testing to obtain a final conclusion about the statements through your code and statistical testing.¶

3.4.1. Hypothetical Statement - 1¶

1. State Your research hypothesis as a null hypothesis and alternate hypothesis.¶

2. Perform an appropriate statistical test¶

3. Business Insight:¶

3.4.2. Hypothetical Statement - 2¶

1. State Your research hypothesis as a null hypothesis and alternate hypothesis.¶

2. Perform an appropriate statistical test¶

3. Business Insight:¶

3.4.3. Hypothetical Statement - 3¶

1. State Your research hypothesis as a null hypothesis and alternate hypothesis.¶

2. Perform an appropriate statistical test¶

3. Business Insight:¶

4. Data Pre-Processing¶

4.1. Handling Missing Values / Null Values¶

4.2. Handling Outliers: Detection and Treatment Strategies¶

4.2.1. Perform outlier detection:¶

Chart-12. Plotting box plots for all numerical variable¶

4.2.2. Calculate the number of outliers and their percentage:¶

4.2.3. Outlier removal operation:¶

4.2.4. After the outliers were removed:¶

Chart-13. Boxplot Comparison (Before and After)¶

5. Feature Engineering¶

5.1. Feature Selection¶

5.1.1. Encoding Categorical Variables¶

5.1.2. Correlation Heatmap of Features¶

Chart-14. Correlation Heatmap of Features¶

5.1.3. Variance Inflation Factor¶

VIF (Variance Inflation Factor):¶